수학자 표정 봐 미쳐 내가 잡아줬지 소숫점 | 파인만 포인트 (feynman point, six nines in pi)

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원주율 파이는 무리수이므로 규칙성이 없어보이는데요. 

신기하게도 소숫점 아래 762번째 자리부터 9가 6개나 연속된 구간이 있습니다.

20세기 최고의 물리학자라고 일컬어지는 리처드 파인만이 이 구간까지 원주율을 외우기 좋아했다는데서 파인만 포인트라 불리고 있습니다.

이 외에도 193034번째부터도 9가 6번

222,299번째부터는 8이 6번

244,453번째부터는 5가 6번

252,499번째부터는 6이 6번나옵니다.

 

이 외에도 더 많은 연속열들이 있는데

이는 우연일까요? 아니면 필연일까요?

 

7번 연속으로 같은 숫자가 나오는 구간 정리 - https://oeis.org/search?q=Starting+positions+of+strings+of+seven&language=english&go=Search

 

Starting positions of strings of six 0's in the decimal expansion of Pi

1699927, 2328783, 2609392, 3794572, 3794573, 7257528, 10359803, 10976114, 11406224, 12344362, 13310436, 13310437, 14240591, 14615851, 14679006, 15603186, 18195375, 18512360, 19413548, 22065197, 23022835, 23247316, 24195722, 24213637, 25051110, 26263951, 28321017
 

Starting positions of strings of six 1's in the decimal expansion of Pi.

255945, 2645268, 3218870, 4657555, 4657556, 5130874, 5425806, 5961931, 6653783, 9036112, 11867965, 13249047, 13255651, 15684440, 18548887, 20316848, 22107705, 22564362, 23503699, 28388441, 28580580, 29435972, 30584158, 31678241

 

Starting positions of strings of six 2's in the decimal expansion of Pi.

963024, 1637080, 1795773, 2523356, 3474036, 5463417, 5803105, 7024615, 9742967, 11836401, 12883291, 13208202, 13371031, 15419528, 15783557, 18183625, 19081176, 20031349, 20363606, 20399387, 20735063, 21682696, 25303344, 31104717, 31614606, 32300569, 33093853, 34422277

 

Starting positions of strings of six 3's in the decimal expansion of Pi.

710100, 710101, 1129019, 3204765, 3204766, 4098542, 4640063, 5524958, 9831707, 10985154, 12376276, 12469058, 12469059, 13230524, 13247803, 15239977, 18216168, 18216169, 19175682, 19175683, 22562616, 23375381, 24287401, 25841185, 27090294, 28715870, 29796271, 29956363

 

Starting positions of strings of six 4's in the decimal expansion of Pi.

828499, 1264270, 1691163, 3280219, 3311569, 3552343, 6252652, 6885738, 7282004, 10049065, 10549618, 10567078, 11588274, 11793700, 12376485, 14302933, 15107731, 15408837, 16027040, 16963877, 17122307, 17893953, 17893954, 18125464, 18681327, 22931745, 22931746, 22931747

 

Starting positions of strings of six 5's in the decimal expansion of Pi.

244453, 253209, 419997, 3517236, 3517237, 5168161, 5892331, 6381473, 7449552, 9325203, 9325204, 9824810, 10519242, 10519243, 12662227, 12687789, 13088126, 14714103, 15859192, 16767908, 18109837, 21826210, 22619752, 23198726

 

Starting positions of strings of six 6's in the decimal expansion of Pi.

252499, 3813777, 4213896, 5107308, 7114978, 7670945, 8054669, 8209165, 8209166, 8555404, 9711986, 12228698, 12797318, 14486103, 14646906, 14927392, 16002486, 16897961, 17911798, 18696860, 18696861, 19506065, 19715001, 19715002

 

Starting positions of strings of six 7's in the decimal expansion of Pi.

399579, 452071, 1006927, 2309218, 2376567, 3346228, 3346229, 3775287, 3775288, 4431395, 5267503, 6052100, 6314342, 9569325, 9891884, 10567998, 12306442, 12389948, 13761115, 13841285, 13912716, 14233532, 14233533, 14445874

 

Starting positions of strings of six 8's in the decimal expansion of Pi.

222299, 2418533, 3019042, 3147134, 3604524, 4722613, 4722614, 5716972, 5765299, 6428161, 6443216, 7747736, 7764272, 7820866, 7820867, 8314999, 8368234, 9386660, 9776789, 11630694, 11887882, 12134905, 12378262, 15836193, 17052618

 

Starting positions of strings of six 9's in the decimal expansion of Pi.

762, 193034, 1722776, 1722777, 1985813, 2878443, 3062881, 3389380, 3389381, 3529731, 4313727, 4313728, 5466169, 5466170, 6951812, 7298585, 8498459, 11295221, 12943563, 13347753, 14388723, 14593770, 14593771, 14670295, 15256174, 15256175, 15866194, 16192557, 16785635

 

출처 - https://oeis.org

원주율 100만 자릿수 - https://angio.net/pi/digits/pi1000000.txt

원주율에서 내 생일 찾기 - https://angio.net/pi/bigpi.cgi