确定给定的级数是否收敛

Question

确定给定的级数是否收敛

如果一个给定的数字是偶数-除以二。如果一个给定的数字是奇数-乘以3并加1。

您需要对从10到1000的所有数字重复应用此逻辑，并说明对于给定的数字，序列是否收敛到1。如果它收敛了，那么它会在几个步骤中收敛？

for (var x=1; x <=15; x++) {
    if (x === 0 ) {
        console.log(x + " is even ");
    } else if (x % 2 === 0) {
        console.log(x + " is even");
    } 
    else {
        console.log(x + " is odd");
    }
}

Answer 1

考虑使用for循环：

// https://en.wikipedia.org/w/index.php?title=Hailstone_sequence
const hailstone = n => {
    let seqLength = 1;
    while (n != 1) {
        n = n & 1 ? 3 * n + 1 : n / 2; // https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Conditional_Operator
        seqLength++;
    }
    return seqLength;
}

for (let n = 10; n <= 1000; n++) {
    const stepsToConverge = hailstone(n);
    console.log(`n=${n} stepsToConverge=${stepsToConverge}`);
}

输出：

n=10 stepsToConverge=7
n=11 stepsToConverge=15
n=12 stepsToConverge=10
n=13 stepsToConverge=10
n=14 stepsToConverge=18
n=15 stepsToConverge=18
n=16 stepsToConverge=5
n=17 stepsToConverge=13
n=18 stepsToConverge=21
n=19 stepsToConverge=21
n=20 stepsToConverge=8
n=21 stepsToConverge=8
n=22 stepsToConverge=16
n=23 stepsToConverge=16
n=24 stepsToConverge=11
n=25 stepsToConverge=24
n=26 stepsToConverge=11
n=27 stepsToConverge=112
n=28 stepsToConverge=19
n=29 stepsToConverge=19
n=30 stepsToConverge=19
n=31 stepsToConverge=107
n=32 stepsToConverge=6
n=33 stepsToConverge=27
n=34 stepsToConverge=14
n=35 stepsToConverge=14
n=36 stepsToConverge=22
n=37 stepsToConverge=22
n=38 stepsToConverge=22
n=39 stepsToConverge=35
n=40 stepsToConverge=9
n=41 stepsToConverge=110
n=42 stepsToConverge=9
n=43 stepsToConverge=30
n=44 stepsToConverge=17
n=45 stepsToConverge=17
n=46 stepsToConverge=17
n=47 stepsToConverge=105
n=48 stepsToConverge=12
n=49 stepsToConverge=25
n=50 stepsToConverge=25
n=51 stepsToConverge=25
n=52 stepsToConverge=12
n=53 stepsToConverge=12
n=54 stepsToConverge=113
n=55 stepsToConverge=113
n=56 stepsToConverge=20
n=57 stepsToConverge=33
n=58 stepsToConverge=20
n=59 stepsToConverge=33
n=60 stepsToConverge=20
n=61 stepsToConverge=20
n=62 stepsToConverge=108
n=63 stepsToConverge=108
n=64 stepsToConverge=7
n=65 stepsToConverge=28
n=66 stepsToConverge=28
n=67 stepsToConverge=28
n=68 stepsToConverge=15
n=69 stepsToConverge=15
n=70 stepsToConverge=15
n=71 stepsToConverge=103
n=72 stepsToConverge=23
n=73 stepsToConverge=116
n=74 stepsToConverge=23
n=75 stepsToConverge=15
n=76 stepsToConverge=23
n=77 stepsToConverge=23
n=78 stepsToConverge=36
n=79 stepsToConverge=36
n=80 stepsToConverge=10
n=81 stepsToConverge=23
n=82 stepsToConverge=111
n=83 stepsToConverge=111
n=84 stepsToConverge=10
n=85 stepsToConverge=10
n=86 stepsToConverge=31
n=87 stepsToConverge=31
n=88 stepsToConverge=18
n=89 stepsToConverge=31
n=90 stepsToConverge=18
n=91 stepsToConverge=93
n=92 stepsToConverge=18
n=93 stepsToConverge=18
n=94 stepsToConverge=106
n=95 stepsToConverge=106
n=96 stepsToConverge=13
n=97 stepsToConverge=119
n=98 stepsToConverge=26
n=99 stepsToConverge=26
n=100 stepsToConverge=26
n=101 stepsToConverge=26
n=102 stepsToConverge=26
n=103 stepsToConverge=88
n=104 stepsToConverge=13
n=105 stepsToConverge=39
n=106 stepsToConverge=13
n=107 stepsToConverge=101
n=108 stepsToConverge=114
n=109 stepsToConverge=114
n=110 stepsToConverge=114
n=111 stepsToConverge=70
n=112 stepsToConverge=21
n=113 stepsToConverge=13
n=114 stepsToConverge=34
n=115 stepsToConverge=34
n=116 stepsToConverge=21
n=117 stepsToConverge=21
n=118 stepsToConverge=34
n=119 stepsToConverge=34
n=120 stepsToConverge=21
n=121 stepsToConverge=96
n=122 stepsToConverge=21
n=123 stepsToConverge=47
n=124 stepsToConverge=109
n=125 stepsToConverge=109
n=126 stepsToConverge=109
n=127 stepsToConverge=47
n=128 stepsToConverge=8
n=129 stepsToConverge=122
n=130 stepsToConverge=29
n=131 stepsToConverge=29
n=132 stepsToConverge=29
n=133 stepsToConverge=29
n=134 stepsToConverge=29
n=135 stepsToConverge=42
n=136 stepsToConverge=16
n=137 stepsToConverge=91
n=138 stepsToConverge=16
n=139 stepsToConverge=42
n=140 stepsToConverge=16
n=141 stepsToConverge=16
n=142 stepsToConverge=104
n=143 stepsToConverge=104
n=144 stepsToConverge=24
n=145 stepsToConverge=117
n=146 stepsToConverge=117
n=147 stepsToConverge=117
n=148 stepsToConverge=24
n=149 stepsToConverge=24
n=150 stepsToConverge=16
n=151 stepsToConverge=16
n=152 stepsToConverge=24
n=153 stepsToConverge=37
n=154 stepsToConverge=24
n=155 stepsToConverge=86
n=156 stepsToConverge=37
n=157 stepsToConverge=37
n=158 stepsToConverge=37
n=159 stepsToConverge=55
n=160 stepsToConverge=11
n=161 stepsToConverge=99
n=162 stepsToConverge=24
n=163 stepsToConverge=24
n=164 stepsToConverge=112
n=165 stepsToConverge=112
n=166 stepsToConverge=112
n=167 stepsToConverge=68
n=168 stepsToConverge=11
n=169 stepsToConverge=50
n=170 stepsToConverge=11
n=171 stepsToConverge=125
n=172 stepsToConverge=32
n=173 stepsToConverge=32
n=174 stepsToConverge=32
n=175 stepsToConverge=81
n=176 stepsToConverge=19
n=177 stepsToConverge=32
n=178 stepsToConverge=32
n=179 stepsToConverge=32
n=180 stepsToConverge=19
n=181 stepsToConverge=19
n=182 stepsToConverge=94
n=183 stepsToConverge=94
n=184 stepsToConverge=19
n=185 stepsToConverge=45
n=186 stepsToConverge=19
n=187 stepsToConverge=45
n=188 stepsToConverge=107
n=189 stepsToConverge=107
n=190 stepsToConverge=107
n=191 stepsToConverge=45
n=192 stepsToConverge=14
n=193 stepsToConverge=120
n=194 stepsToConverge=120
n=195 stepsToConverge=120
n=196 stepsToConverge=27
n=197 stepsToConverge=27
n=198 stepsToConverge=27
n=199 stepsToConverge=120
n=200 stepsToConverge=27
n=201 stepsToConverge=19
n=202 stepsToConverge=27
n=203 stepsToConverge=40
n=204 stepsToConverge=27
n=205 stepsToConverge=27
n=206 stepsToConverge=89
n=207 stepsToConverge=89
n=208 stepsToConverge=14
n=209 stepsToConverge=40
n=210 stepsToConverge=40
n=211 stepsToConverge=40
n=212 stepsToConverge=14
n=213 stepsToConverge=14
n=214 stepsToConverge=102
n=215 stepsToConverge=102
n=216 stepsToConverge=115
n=217 stepsToConverge=27
n=218 stepsToConverge=115
n=219 stepsToConverge=53
n=220 stepsToConverge=115
n=221 stepsToConverge=115
n=222 stepsToConverge=71
n=223 stepsToConverge=71
n=224 stepsToConverge=22
n=225 stepsToConverge=53
n=226 stepsToConverge=14
n=227 stepsToConverge=14
n=228 stepsToConverge=35
n=229 stepsToConverge=35
n=230 stepsToConverge=35
n=231 stepsToConverge=128
n=232 stepsToConverge=22
n=233 stepsToConverge=84
n=234 stepsToConverge=22
n=235 stepsToConverge=128
n=236 stepsToConverge=35
n=237 stepsToConverge=35
n=238 stepsToConverge=35
n=239 stepsToConverge=53
n=240 stepsToConverge=22
n=241 stepsToConverge=22
n=242 stepsToConverge=97
n=243 stepsToConverge=97
n=244 stepsToConverge=22
n=245 stepsToConverge=22
n=246 stepsToConverge=48
n=247 stepsToConverge=48
n=248 stepsToConverge=110
n=249 stepsToConverge=48
n=250 stepsToConverge=110
n=251 stepsToConverge=66
n=252 stepsToConverge=110
n=253 stepsToConverge=110
n=254 stepsToConverge=48
n=255 stepsToConverge=48
n=256 stepsToConverge=9
n=257 stepsToConverge=123
n=258 stepsToConverge=123
n=259 stepsToConverge=123
n=260 stepsToConverge=30
n=261 stepsToConverge=30
n=262 stepsToConverge=30
n=263 stepsToConverge=79
n=264 stepsToConverge=30
n=265 stepsToConverge=123
n=266 stepsToConverge=30
n=267 stepsToConverge=22
n=268 stepsToConverge=30
n=269 stepsToConverge=30
n=270 stepsToConverge=43
n=271 stepsToConverge=43
n=272 stepsToConverge=17
n=273 stepsToConverge=30
n=274 stepsToConverge=92
n=275 stepsToConverge=92
n=276 stepsToConverge=17
n=277 stepsToConverge=17
n=278 stepsToConverge=43
n=279 stepsToConverge=43
n=280 stepsToConverge=17
n=281 stepsToConverge=43
n=282 stepsToConverge=17
n=283 stepsToConverge=61
n=284 stepsToConverge=105
n=285 stepsToConverge=105
n=286 stepsToConverge=105
n=287 stepsToConverge=43
n=288 stepsToConverge=25
n=289 stepsToConverge=30
n=290 stepsToConverge=118
n=291 stepsToConverge=118
n=292 stepsToConverge=118
n=293 stepsToConverge=118
n=294 stepsToConverge=118
n=295 stepsToConverge=56
n=296 stepsToConverge=25
n=297 stepsToConverge=74
n=298 stepsToConverge=25
n=299 stepsToConverge=118
n=300 stepsToConverge=17
n=301 stepsToConverge=17
n=302 stepsToConverge=17
n=303 stepsToConverge=43
n=304 stepsToConverge=25
n=305 stepsToConverge=38
n=306 stepsToConverge=38
n=307 stepsToConverge=38
n=308 stepsToConverge=25
n=309 stepsToConverge=25
n=310 stepsToConverge=87
n=311 stepsToConverge=87
n=312 stepsToConverge=38
n=313 stepsToConverge=131
n=314 stepsToConverge=38
n=315 stepsToConverge=38
n=316 stepsToConverge=38
n=317 stepsToConverge=38
n=318 stepsToConverge=56
n=319 stepsToConverge=56
n=320 stepsToConverge=12
n=321 stepsToConverge=25
n=322 stepsToConverge=100
n=323 stepsToConverge=100
n=324 stepsToConverge=25
n=325 stepsToConverge=25
n=326 stepsToConverge=25
n=327 stepsToConverge=144
n=328 stepsToConverge=113
n=329 stepsToConverge=51
n=330 stepsToConverge=113
n=331 stepsToConverge=25
n=332 stepsToConverge=113
n=333 stepsToConverge=113
n=334 stepsToConverge=69
n=335 stepsToConverge=69
n=336 stepsToConverge=12
n=337 stepsToConverge=113
n=338 stepsToConverge=51
n=339 stepsToConverge=51
n=340 stepsToConverge=12
n=341 stepsToConverge=12
n=342 stepsToConverge=126
n=343 stepsToConverge=126
n=344 stepsToConverge=33
n=345 stepsToConverge=126
n=346 stepsToConverge=33
n=347 stepsToConverge=126
n=348 stepsToConverge=33
n=349 stepsToConverge=33
n=350 stepsToConverge=82
n=351 stepsToConverge=82
n=352 stepsToConverge=20
n=353 stepsToConverge=126
n=354 stepsToConverge=33
n=355 stepsToConverge=33
n=356 stepsToConverge=33
n=357 stepsToConverge=33
n=358 stepsToConverge=33
n=359 stepsToConverge=51
n=360 stepsToConverge=20
n=361 stepsToConverge=46
n=362 stepsToConverge=20
n=363 stepsToConverge=46
n=364 stepsToConverge=95
n=365 stepsToConverge=95
n=366 stepsToConverge=95
n=367 stepsToConverge=46
n=368 stepsToConverge=20
n=369 stepsToConverge=20
n=370 stepsToConverge=46
n=371 stepsToConverge=46
n=372 stepsToConverge=20
n=373 stepsToConverge=20
n=374 stepsToConverge=46
n=375 stepsToConverge=46
n=376 stepsToConverge=108
n=377 stepsToConverge=64
n=378 stepsToConverge=108
n=379 stepsToConverge=59
n=380 stepsToConverge=108
n=381 stepsToConverge=108
n=382 stepsToConverge=46
n=383 stepsToConverge=46
n=384 stepsToConverge=15
n=385 stepsToConverge=33
n=386 stepsToConverge=121
n=387 stepsToConverge=121
n=388 stepsToConverge=121
n=389 stepsToConverge=121
n=390 stepsToConverge=121
n=391 stepsToConverge=121
n=392 stepsToConverge=28
n=393 stepsToConverge=59
n=394 stepsToConverge=28
n=395 stepsToConverge=77
n=396 stepsToConverge=28
n=397 stepsToConverge=28
n=398 stepsToConverge=121
n=399 stepsToConverge=121
n=400 stepsToConverge=28
n=401 stepsToConverge=20
n=402 stepsToConverge=20
n=403 stepsToConverge=20
n=404 stepsToConverge=28
n=405 stepsToConverge=28
n=406 stepsToConverge=41
n=407 stepsToConverge=41
n=408 stepsToConverge=28
n=409 stepsToConverge=41
n=410 stepsToConverge=28
n=411 stepsToConverge=134
n=412 stepsToConverge=90
n=413 stepsToConverge=90
n=414 stepsToConverge=90
n=415 stepsToConverge=134
n=416 stepsToConverge=15
n=417 stepsToConverge=134
n=418 stepsToConverge=41
n=419 stepsToConverge=41
n=420 stepsToConverge=41
n=421 stepsToConverge=41
n=422 stepsToConverge=41
n=423 stepsToConverge=33
n=424 stepsToConverge=15
n=425 stepsToConverge=59
n=426 stepsToConverge=15
n=427 stepsToConverge=54
n=428 stepsToConverge=103
n=429 stepsToConverge=103
n=430 stepsToConverge=103
n=431 stepsToConverge=41
n=432 stepsToConverge=116
n=433 stepsToConverge=28
n=434 stepsToConverge=28
n=435 stepsToConverge=28
n=436 stepsToConverge=116
n=437 stepsToConverge=116
n=438 stepsToConverge=54
n=439 stepsToConverge=54
n=440 stepsToConverge=116
n=441 stepsToConverge=28
n=442 stepsToConverge=116
n=443 stepsToConverge=54
n=444 stepsToConverge=72
n=445 stepsToConverge=72
n=446 stepsToConverge=72
n=447 stepsToConverge=98
n=448 stepsToConverge=23
n=449 stepsToConverge=116
n=450 stepsToConverge=54
n=451 stepsToConverge=54
n=452 stepsToConverge=15
n=453 stepsToConverge=15
n=454 stepsToConverge=15
n=455 stepsToConverge=41
n=456 stepsToConverge=36
n=457 stepsToConverge=129
n=458 stepsToConverge=36
n=459 stepsToConverge=129
n=460 stepsToConverge=36
n=461 stepsToConverge=36
n=462 stepsToConverge=129
n=463 stepsToConverge=129
n=464 stepsToConverge=23
n=465 stepsToConverge=36
n=466 stepsToConverge=85
n=467 stepsToConverge=85
n=468 stepsToConverge=23
n=469 stepsToConverge=23
n=470 stepsToConverge=129
n=471 stepsToConverge=129
n=472 stepsToConverge=36
n=473 stepsToConverge=36
n=474 stepsToConverge=36
n=475 stepsToConverge=28
n=476 stepsToConverge=36
n=477 stepsToConverge=36
n=478 stepsToConverge=54
n=479 stepsToConverge=54
n=480 stepsToConverge=23
n=481 stepsToConverge=49
n=482 stepsToConverge=23
n=483 stepsToConverge=23
n=484 stepsToConverge=98
n=485 stepsToConverge=98
n=486 stepsToConverge=98
n=487 stepsToConverge=142
n=488 stepsToConverge=23
n=489 stepsToConverge=49
n=490 stepsToConverge=23
n=491 stepsToConverge=142
n=492 stepsToConverge=49
n=493 stepsToConverge=49
n=494 stepsToConverge=49
n=495 stepsToConverge=98
n=496 stepsToConverge=111
n=497 stepsToConverge=23
n=498 stepsToConverge=49
n=499 stepsToConverge=49
n=500 stepsToConverge=111
n=501 stepsToConverge=111
n=502 stepsToConverge=67
n=503 stepsToConverge=67
n=504 stepsToConverge=111
n=505 stepsToConverge=62
n=506 stepsToConverge=111
n=507 stepsToConverge=36
n=508 stepsToConverge=49
n=509 stepsToConverge=49
n=510 stepsToConverge=49
n=511 stepsToConverge=62
n=512 stepsToConverge=10
n=513 stepsToConverge=36
n=514 stepsToConverge=124
n=515 stepsToConverge=124
n=516 stepsToConverge=124
n=517 stepsToConverge=124
n=518 stepsToConverge=124
n=519 stepsToConverge=62
n=520 stepsToConverge=31
n=521 stepsToConverge=124
n=522 stepsToConverge=31
n=523 stepsToConverge=124
n=524 stepsToConverge=31
n=525 stepsToConverge=31
n=526 stepsToConverge=80
n=527 stepsToConverge=80
n=528 stepsToConverge=31
n=529 stepsToConverge=31
n=530 stepsToConverge=124
n=531 stepsToConverge=124
n=532 stepsToConverge=31
n=533 stepsToConverge=31
n=534 stepsToConverge=23
n=535 stepsToConverge=23
n=536 stepsToConverge=31
n=537 stepsToConverge=23
n=538 stepsToConverge=31
n=539 stepsToConverge=49
n=540 stepsToConverge=44
n=541 stepsToConverge=44
n=542 stepsToConverge=44
n=543 stepsToConverge=137
n=544 stepsToConverge=18
n=545 stepsToConverge=44
n=546 stepsToConverge=31
n=547 stepsToConverge=31
n=548 stepsToConverge=93
n=549 stepsToConverge=93
n=550 stepsToConverge=93
n=551 stepsToConverge=44
n=552 stepsToConverge=18
n=553 stepsToConverge=137
n=554 stepsToConverge=18
n=555 stepsToConverge=31
n=556 stepsToConverge=44
n=557 stepsToConverge=44
n=558 stepsToConverge=44
n=559 stepsToConverge=88
n=560 stepsToConverge=18
n=561 stepsToConverge=44
n=562 stepsToConverge=44
n=563 stepsToConverge=44
n=564 stepsToConverge=18
n=565 stepsToConverge=18
n=566 stepsToConverge=62
n=567 stepsToConverge=62
n=568 stepsToConverge=106
n=569 stepsToConverge=57
n=570 stepsToConverge=106
n=571 stepsToConverge=31
n=572 stepsToConverge=106
n=573 stepsToConverge=106
n=574 stepsToConverge=44
n=575 stepsToConverge=44
n=576 stepsToConverge=26
n=577 stepsToConverge=31
n=578 stepsToConverge=31
n=579 stepsToConverge=31
n=580 stepsToConverge=119
n=581 stepsToConverge=119
n=582 stepsToConverge=119
n=583 stepsToConverge=31
n=584 stepsToConverge=119
n=585 stepsToConverge=57
n=586 stepsToConverge=119
n=587 stepsToConverge=119
n=588 stepsToConverge=119
n=589 stepsToConverge=119
n=590 stepsToConverge=57
n=591 stepsToConverge=57
n=592 stepsToConverge=26
n=593 stepsToConverge=75
n=594 stepsToConverge=75
n=595 stepsToConverge=75
n=596 stepsToConverge=26
n=597 stepsToConverge=26
n=598 stepsToConverge=119
n=599 stepsToConverge=119
n=600 stepsToConverge=18
n=601 stepsToConverge=57
n=602 stepsToConverge=18
n=603 stepsToConverge=70
n=604 stepsToConverge=18
n=605 stepsToConverge=18
n=606 stepsToConverge=44
n=607 stepsToConverge=44
n=608 stepsToConverge=26
n=609 stepsToConverge=132
n=610 stepsToConverge=39
n=611 stepsToConverge=39
n=612 stepsToConverge=39
n=613 stepsToConverge=39
n=614 stepsToConverge=39
n=615 stepsToConverge=70
n=616 stepsToConverge=26
n=617 stepsToConverge=132
n=618 stepsToConverge=26
n=619 stepsToConverge=132
n=620 stepsToConverge=88
n=621 stepsToConverge=88
n=622 stepsToConverge=88
n=623 stepsToConverge=132
n=624 stepsToConverge=39
n=625 stepsToConverge=26
n=626 stepsToConverge=132
n=627 stepsToConverge=132
n=628 stepsToConverge=39
n=629 stepsToConverge=39
n=630 stepsToConverge=39
n=631 stepsToConverge=39
n=632 stepsToConverge=39
n=633 stepsToConverge=31
n=634 stepsToConverge=39
n=635 stepsToConverge=31
n=636 stepsToConverge=57
n=637 stepsToConverge=57
n=638 stepsToConverge=57
n=639 stepsToConverge=132
n=640 stepsToConverge=13
n=641 stepsToConverge=52
n=642 stepsToConverge=26
n=643 stepsToConverge=26
n=644 stepsToConverge=101
n=645 stepsToConverge=101
n=646 stepsToConverge=101
n=647 stepsToConverge=39
n=648 stepsToConverge=26
n=649 stepsToConverge=145
n=650 stepsToConverge=26
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