Displaying 1-10 of 20 results found.
Positions of the digit '2' in the decimal expansion of Pi (where positions 0, 1, 2,... refer to the digits 3, 1, 4,...).
+10
26
6, 16, 21, 28, 33, 53, 63, 73, 76, 83, 89, 93, 102, 112, 114, 135, 136, 140, 149, 160, 165, 173, 185, 186, 203, 221, 229, 241, 244, 260, 275, 280, 289, 292, 298, 302, 326, 329, 333, 335, 337, 354, 374, 380, 406, 423, 435, 456, 462, 477, 479, 484, 485, 500
COMMENTS
The first few primes in this sequence are 53, 73, 83, 89, 149, 173, 229, 241, 337, 479, 571, 613, 661, 757, 829, 877, 911, 977, 991, ... - M. F. Hasler, Jul 28 2024
FORMULA
a(n) ~ 10*n if Pi is normal, as generally assumed. - M. F. Hasler, Jul 28 2024
MATHEMATICA
Flatten @ Position[ RealDigits[Pi - 3, 10, 500][[1]], 2] (* Robert G. Wilson v, Mar 07 2011 *)
PROG
(PARI) A037001_upto(N=999, d=2)={localprec(N+20); [i-1|i<-[1..#N=digits(Pi\10^-N)], N[i]==d]} \\ M. F. Hasler, Jul 28 2024
CROSSREFS
Cf. A000796 (decimal expansion (or digits) of Pi).
Cf. A053746 (= a(n) + 1: the same with different offset).
Cf. A037000, A037002, A037003, A037004, A037005, A036974, A037006, A037007, A037008 (similar for digits 1, ..., 9 and 0).
Cf. A176341: first occurrence of n in Pi's digits.
AUTHOR
Nicolau C. Saldanha (nicolau(AT)mat.puc-rio.br)
Position of the first occurrence of exactly n consecutive '9's in a row in the decimal expansion of Pi.
+10
24
5, 44, 2949, 17988, 19446, 762, 1722776, 36356642, 564665206, 20148132310, 27014073304, 897831316556, 10542036048450, 5758910552709
CROSSREFS
Cf. A000796: Decimal expansion (or digits) of Pi.
EXTENSIONS
a(12) from Yasumasa Kanada, 2002 and a(13)-a(14) from Shigeru Kondo, 2011, added by Dmitry Petukhov, Dec 27 2019
a(n) is the starting position of the first occurrence of a string of exactly n 6's in the decimal expansion of Pi.
+10
22
7, 117, 2440, 21880, 48439, 252499, 8209165, 55616210, 45681781, 386980412, 32104158792, 1221587715177, 81111117323616
COMMENTS
a(13)-a(16) > 5*10^13, a(17) = 28642224609576. - Dmitry Petukhov, Oct 30 2021
LINKS
Eric Weisstein's World of Mathematics, Pi Digits
a(n) is the starting position of the first occurrence of a string of at least n 1's in the decimal expansion of Pi.
+10
21
1, 94, 153, 12700, 32788, 255945, 4657555, 159090113, 812432526, 3961184001, 15647738228, 1041032609981, 3907688331257, 68635742334547
COMMENTS
Presently identical to A096755, which is the first occurrences of exactly n 1's in the digits of Pi. Will differ as soon as there's some a(n) = a(n+1) and equivalently, A035117(n) > A035117(n+1). - M. F. Hasler, Mar 17 2017
CROSSREFS
Cf. A000796 (decimal expansion (or digits) of Pi).
Cf. A176341 (first occurrence of n in Pi's digits).
AUTHOR
Leonardo Bitran (lbitran(AT)reuna.cl)
EXTENSIONS
More terms from Colin Martin (cbmartin(AT)tpg.com.au), Mar 03 2002
a(12) from Yasumasa Kanada Laboratory, 2002 and a(13) from Shigeru Kondo, 2011, added by Dmitry Petukhov, Dec 27 2019
a(n) is the starting position of the first occurrence of a string of at least n '0's in the decimal expansion of Pi.
+10
21
32, 307, 601, 13390, 17534, 1699927, 3794572, 172330850, 2542542102, 8324296435, 371247087572, 1755524129973, 3186699229890, 6381820482331
COMMENTS
At least up to a(10), also the starting position of the first occurrence of a string of exactly n '0's in the decimal expansion of Pi, cf. A096764. - M. F. Hasler, Mar 19 2017, edited Sep 03 2017
REFERENCES
Shigeru Kondo, calculation of Pi to 12.8 * 10^9 digits, using the program PiFast of Xavier Gourdon
LINKS
Eric Weisstein's World of Mathematics, Pi Digits
CROSSREFS
Cf. A000796: Decimal expansion (or digits) of Pi.
EXTENSIONS
More terms from Colin B. Martin (martinc(AT)ram.net.au), Nov 25 2001
Index of first occurrence of just n consecutive fives in a row in the decimal expansion of Pi.
+10
21
4, 130, 177, 33172, 24466, 244453, 3517236, 168743355, 5050944965, 7644991298, 157675736216, 1618922020656, 9593946215340, 7604259624808
Position of first occurrence of exactly n consecutive sevens in a row in the decimal expansion of Pi.
+10
21
13, 559, 4575, 1589, 162248, 399579, 3346228, 82144203, 24658601, 22869046249, 165431035708, 368299898266, 10541103245815, 14793486898235, 46970519777308
CROSSREFS
Cf. A000796 (decimal expansion (or digits) of Pi).
Starting position of the first occurrence of a string of at least n '9's in the decimal expansion of Pi.
+10
20
5, 44, 762, 762, 762, 762, 1722776, 36356642, 564665206, 20148132310, 27014073304, 897831316556, 5758910552709, 5758910552709
COMMENTS
Pi digits 3,1,4,... are indexed 0,1,2,... Note that this is different from other sequences such as A049522, A084073 which use indices 1,2,3,... For example, the position of the curious accumulation of six 9s is called 762 here; the same position is called 763 in A049522, A084073. - Jeppe Stig Nielsen, Aug 21 2017
LINKS
David G. Andersen, The Pi-Search Page. (Yields, as of today, an incorrect result of 66780105 for the first occurrence of eight "9"s. - M. F. Hasler, Mar 19 2017)
Eric Weisstein's World of Mathematics, Pi Digits
MATHEMATICA
Module[{m, nn = 7}, m = First@ RealDigits@ N[Pi, 10^nn]; Array[ SequencePosition[m, ConstantArray[9, #]][[1, 1]] - 1 &, nn]] (* Michael De Vlieger, Mar 20 2017 *)
CROSSREFS
Cf. A000796: Decimal expansion (or digits) of Pi.
EXTENSIONS
More terms from Colin Martin (cbmartin(AT)tpg.com.au), Mar 03 2002
a(12) from Yasumasa Kanada Laboratory, 2002 and a(13)-a(14) from Shigeru Kondo, 2011 added by Dmitry Petukhov, Dec 23 2019
Index of first occurrence of exactly n consecutive twos in a row in the decimal expansion of Pi.
+10
20
6, 135, 1735, 4902, 65260, 963024, 82599811, 175820910, 1270311937, 20717271655, 225023890967, 1479132847647, 5547233660249
COMMENTS
Presently identical to A050281, but it can be expected that the two will eventually differ, namely, as soon as a(n) > a(n+1) and A050281(n) = A050281(n+1).
a(10) > 2*10^9, according to the SubIdiom.com search engine. - M. F. Hasler, Apr 13 2019
EXAMPLE
Pi = 3.1415926... has a "run" of exactly one '2' in the 6th place after the decimal point, therefore a(1) = 6.
Index of first occurrence of exactly n consecutive threes in a row in the decimal expansion of Pi.
+10
20
9, 24, 1698, 66846, 28467, 1129019, 710100, 36488176, 2011485307, 4663739959, 60422218263, 1379574176590, 26258139334603
CROSSREFS
Cf. A050282 (same for at least three 3s); A050279, A035117, A096756, A096758, A096759, A096760, A096761, A096762, A096763 (analog for digits 0, 1, 2, 4, ...).
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