A053753 -id:A053753 - cp's OEIS frontend

A037007 Positions of the digit '9' in the decimal expansion of Pi, where positions 0, 1, 2,... correspond to digits 3, 1, 4, ....

5, 12, 14, 30, 38, 42, 44, 45, 55, 58, 62, 79, 80, 100, 122, 129, 144, 169, 180, 187, 190, 193, 199, 208, 214, 247, 249, 259, 284, 294, 328, 331, 336, 341, 353, 356, 388, 391, 399, 414, 416, 418, 422, 433, 440, 459, 460, 465, 482, 487, 496, 498, 501, 527

Offset: 1

Nicolau C. Saldanha (nicolau(AT)mat.puc-rio.br)

Primes in this sequence are 5, 79, 193, 199, 331, 353, 433, 487, 941, ... - M. F. Hasler, Jul 29 2024

			The first digit '9' occurs in 3.1415926... at the 5th place after the decimal point, whence a(1) = 5.

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..369 from M. F. Hasler)
Eric Weisstein's World of Mathematics, Pi Digits.
Index entries for sequences related to the number Pi

Cf. A000796 (decimals of Pi).
Cf. A053753 (variant with all values increased by 1).
Cf. A037000, A037001, A037002, A037003, A037004, A037005, A036974, A037006, A037008 (similar for digits 1, ..., 8 and 0).
Cf. A048940, A096763 (starting position of at least/exactly n '9's).

Flatten @ Position[ RealDigits[Pi - 3, 10, 500][[1]], 9] (* Robert G. Wilson v, Mar 07 2011 *)

A037007_upto(N=999, d=9)={localprec(N+20); [i-1|i<-[1..#N=digits(Pi\10^-N)], N[i]==d]} \\ M. F. Hasler, Jul 29 2024

a(n) = A053753(n) - 1. - M. F. Hasler, Mar 20 2017

a(n) ~ 10*n if Pi is normal (as generally assumed, but yet unproved). - M. F. Hasler, Jul 29 2024

A096567 First digit to appear n times in the base-10 expansion of Pi.

Original entry on oeis.org

3, 1, 5, 3, 3, 3, 3, 3, 3, 9, 9, 9, 9, 9, 8, 8, 8, 8, 8, 8, 8, 8, 8, 2, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 4, 4, 8, 2, 2, 8, 2, 4, 4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Matthew Vandermast, Jun 26 2004

The number 7 finally appears as a(32344). - T. D. Noe, Sep 13 2012

The number 6 appears for the first time as a(99032274). - Kester Habermann, Feb 01 2021

			a(3) = 5 because 5 is the first digit to appear 3 times in the decimal expansion of Pi = 3.141(5)926(5)3(5)... - _Bobby Jacobs_, Aug 30 2017

Jianing Song, Table of n, a(n) for n = 1..32373 (added to include the first occurrences of 0 and 7, first 10000 terms from T. D. Noe)

Cf. A000796, A014976, A053745-A053753, A096566.
Cf. A195138, A195139, A195141, A280811.
Cf. A276686, A276992, A276993, A277171, A291599, A291600.

nn = 1000; t = {}; d = RealDigits[Pi, 10, nn][[1]]; dCnt = Table[0, {10}]; cnt = 1; Do[b = ++dCnt[[1 + d[[n]]]]; If[b == cnt, AppendTo[t, d[[n]]]; cnt++], {n, nn}]; t (* T. D. Noe, Sep 13 2012 *)

More terms from David Wasserman, Nov 16 2007

A014976 Successive locations of zeros in decimal expansion of Pi (where locations 1, 2, 3, ... correspond to digits 3, 1, 4, ...).

Original entry on oeis.org

33, 51, 55, 66, 72, 78, 86, 98, 107, 117, 122, 129, 133, 147, 160, 165, 168, 177, 196, 208, 246, 249, 265, 271, 288, 292, 308, 309, 312, 328, 331, 341, 358, 361, 362, 367, 370, 376, 399, 404, 409, 422, 444, 452, 494, 514, 521, 524, 544, 546, 553, 558, 562, 597, 602, 603, 604, 619, 639, 658

Offset: 1

Bagirath R. Krishnamachari (bagi(AT)callisto.miel.mot.com)

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for sequences related to the number Pi

Cf. A000796 (decimal expansion (or digits) of Pi).
Cf. A053745 - A053753 (similar for digits 1 through 9).
Cf. A037008 for a variant with all values decreased by 1.
See A088563 for primes in this sequence.

f := proc(n) if pi[n]=0 then n fi; end;[seq(f(i),i=1..2000)]; # where pi is an array with the digits of Pi. - Simon Plouffe [Corrected by Neven Juric, Jul 08 2008]

Flatten[ Position[ RealDigits[Pi, 10, 660] [[1]], 0]] (* Robert G. Wilson v, Mar 19 2004 *)

A014976_upto(N=999)={localprec(N+20); select(d->!d, digits(Pi\10^-N), 1)} \\ Returns a "Vecsmall": use Vec(...) if needed, or alternatively: {...; [i|i<-[1..#N=digits(Pi\10^-N)], !N[i]]}. - M. F. Hasler, Jul 28 2024

a(n) = A037008(n) + 1. - Georg Fischer, May 31 2021

More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)

A053745 Positions of '1's in the decimal expansion of Pi (where positions 1,2,3,... refer to the digits 3,1,4,...).

Original entry on oeis.org

2, 4, 38, 41, 50, 69, 95, 96, 104, 111, 139, 149, 154, 155, 156, 164, 169, 175, 176, 199, 207, 221, 239, 244, 247, 251, 270, 282, 296, 298, 315, 320, 325, 343, 345, 363, 364, 382, 386, 391, 394, 396, 397, 418

Offset: 1

Simon Plouffe, Feb 20 2000

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for sequences related to the number Pi

Cf. A014976, A053746 - A053753 (the same for digits 0, ..., 9).

Cf. A088565 (primes in this sequence), A000796 (decimal digits of Pi).

Flatten[Position[RealDigits[Pi, 10, 1000][[1]], 1]] (* Vincenzo Librandi, Oct 07 2013 *)

A053745_upto(N=444, d=1)={localprec(N+20); [i|i<-[1..#N=digits(Pi\10^-N)], N[i]==d]} \\ M. F. Hasler, Jul 29 2024, replacing earlier code from 2017

a(n) = 1 + A037000(n), a variant where position 1 is the first digit after the decimal point. - M. F. Hasler, Mar 20 2017

a(n) ~ 10*n if Pi is normal (as generally assumed but yet unproved). - M. F. Hasler, Jul 29 2024

A053746 Positions of '2's in the decimal expansion of Pi, where positions 1, 2, 3, ... correspond to digits 3, 1, 4, ...

Original entry on oeis.org

7, 17, 22, 29, 34, 54, 64, 74, 77, 84, 90, 94, 103, 113, 115, 136, 137, 141, 150, 161, 166, 174, 186, 187, 204, 222, 230, 242, 245, 261, 276, 281, 290, 293, 299, 303, 327, 330, 334, 336, 338, 355, 375, 381, 407

Offset: 1

Simon Plouffe, Feb 20 2000

See A037001 for the variant where digits 3, 1, 4, ... correspond to positions 0, 1, 2, ... - M. F. Hasler, Jul 28 2024

			Pi = 3.1415926... where the first '2' occurs as the 7th digit.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for sequences related to the number Pi

Cf. A000796 (decimal expansion (or digits) of Pi).
Cf. A037001 (= a(n) - 1: the same with different offset).
Cf. A053745 - A053753 (similar for digits 1 through 9).
Cf. A035117 (first occurrence of at least n '1's), A050281 (n '2's), A050282, A050283, A050284, A050286, A050287, A048940 (n '9's).
Cf. A096755 (first occurrence of exactly n '1's), A096756, A096757, A096758, A096759, A096760, A096761, A096762, A096763 (exactly n '9's), A050279 (exactly n '0's).
Cf. A121280 = A068987 - 1: position of "123...n" in Pi's decimals.
Cf. A176341: first occurrence of n in Pi's digits.
Cf. A088566 (primes in this sequence).

Flatten[Position[RealDigits[Pi, 10, 1000][[1]], 2]] (* Vincenzo Librandi, Oct 07 2013 *)

A053746_upto(N=999)={localprec(N+20); select(d->d==2, digits(Pi\10^-N), 1)} \\ M. F. Hasler, Jul 28 2024

a(n) = A037001(n) + 1. - Georg Fischer, May 31 2021

Changed offset from 0 to 1 by Vincenzo Librandi, Oct 07 2013

A096566 a(n) = concatenation of 10 distinct decimal digits in order of n-th appearance in the base-10 expansion of Pi.

Original entry on oeis.org

3145926870, 1539284670, 5932648170, 3295841670, 3289517460, 3958247160, 3945286017, 3942865107, 3928461057, 9382461057, 9832460517, 9832640517, 9823460517, 9823450167, 8293415067, 8923410567, 8239401567, 8249310567

Offset: 1

Matthew Vandermast, Jun 26 2004

Maximal information-based nonparametric exploration statistical analysis program (MINE), which I applied "pairwise" to the first 62 terms, shows high values (up to 1) of the maximal information coefficient (MIC), which is a measure of two-variable dependence designed specifically for rapid exploration of many-dimensional data sets - see supplied links. - Alexander R. Povolotsky, Sep 07 2012

Computationally intractable question: what is the last term to appear, assuming all 9*9! terms eventually show up? - Charles R Greathouse IV, Sep 07 2012

Alexander R. Povolotsky, Table of n, a(n) for n = 1..62
Alexander R. Povolotsky, Trends in the distribution of reordered digits of Pi, (question on stackexchange.com)

Cf. A000796, A014976, A053745-A053753, A096567.

A349551 Rectangular array with ten rows, read by falling antidiagonals: row k gives positions of k in the decimal expansion (A000796) of Pi.

Original entry on oeis.org

33, 51, 2, 55, 4, 7, 66, 38, 17, 1, 72, 41, 22, 10, 3, 78, 50, 29, 16, 20, 5, 86, 69, 34, 18, 24, 9, 8, 98, 95, 54, 25, 37, 11, 21, 14, 107, 96, 64, 26, 58, 32, 23, 30, 12, 117, 104, 74, 28, 60, 49, 42, 40, 19, 6

Offset: 0

Clark Kimberling, Dec 17 2021

Every positive integer occurs exactly once.

It is assumed that each digit occurs infinitely many times in A000796.

			(Base-10 digits of Pi) = (3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8, 4, 6, 2, 6, 4, 3, 3, 8, 3, 2, 7, 9, 5, 0, ...); the position of the first 0 is 33, so the first term in row 0 is 33.
Corner:
  33, 51, 55, 66, 72, 78, 86, 98,  107,  117, 122, ... A014976
   2,  4, 38, 41, 50, 69, 95, 96,  104,  111, 139, ... A053745
   7, 17, 22, 29, 34, 54, 64, 74,   77,   84,  90, ... A053746
   1, 10, 16, 18, 25, 26, 28, 44,   47,   65,  87, ... A053747
   3, 20, 24, 37, 58, 60, 61, 71,   88,   93, 105, ... A053748
   5,  9, 11, 32, 49, 52, 62, 91,  110,  131, 132, ... A053749
   8, 21, 23, 42, 70, 73, 76, 83,   99,  109, 118, ... A053750
  14, 30, 40, 48, 57, 67, 97, 100, 121,  140, 157, ... A053751
  12, 19, 27, 35, 36, 53, 68, 75,   79,   82,  85, ... A053752
   6, 13, 15, 31, 39, 43, 45, 46,   56,   59,  63, ... A053753

Index entries for sequences that are permutations of the natural numbers

Cf. A000796, A014976, A053745-A053753, A032445 (includes column 1).

r = RealDigits[Pi, 10, 200][[1]]
t = Table[Flatten[Position[r, n]], {n, 0, 9}]
TableForm[t]  (* A349551 array *)
Flatten[Table[t[[n - k + 1, k]], {n, 10}, {k, n, 1, -1}]] (* A349551 sequence *)

A108664 In the decimal expansion of Pi, lengths of sublists ending with 9.

Original entry on oeis.org

6, 7, 2, 16, 8, 4, 2, 1, 10, 3, 4, 17, 1, 20, 22, 7, 15, 25, 11, 7, 3, 3, 6, 9, 6, 33, 2, 10, 25, 10, 34, 3, 5, 5, 12, 3, 32, 3, 8, 15, 2, 2, 4, 11, 7, 19, 1, 5, 17, 5, 9, 2, 3, 26, 2, 4, 9, 7, 4, 11, 8, 22, 42, 3, 19, 6, 11, 11, 4, 3, 4, 8, 1, 8, 4, 14, 6, 9, 1, 14, 1, 1, 1, 1, 1, 5, 5, 1, 5, 11

Offset: 1

Zak Seidov, Jun 17 2005

Take the decimal expansion of Pi: s={3,1,4,1,5,9,2,6,5,3,5,8,9,7,9,3, 2,3,8,4,6,2,6,4,3,3,8,3,2,7,9,5,0,2,8,8,4}. Split s into sublists each ending with 9: {{3,1,4,1,5,9}, {2,6,5,3,5,8,9}, {7,9}, {3,2,3,8,4,6,2,6,4,3,3,8,3,2,7,9}, {5,0,2,8,8,4,1,9}}. The sequence gives the lengths of the sublists: 6,7,2,16,8,4,2,1,10,3,4,17,1,20,22,7. Cf. A053753 (positions of 9's in the decimal expansion of Pi).

Cf. A000796, A037007, A053753, A108663, A139727, A014974.

a(n) = A053753(n+1) - A053753(n).

A346122 n times the n-th digit of the decimal expansion of Pi.

Original entry on oeis.org

3, 2, 12, 4, 25, 54, 14, 48, 45, 30, 55, 96, 117, 98, 135, 48, 34, 54, 152, 80, 126, 44, 138, 96, 75, 78, 216, 84, 58, 210, 279, 160, 0, 68, 280, 288, 148, 38, 351, 280, 41, 252, 387, 132, 405, 414, 141, 336, 245, 50, 0, 260, 424, 108, 0, 504, 399, 232, 531

Offset: 1

Harvey P. Dale, Jul 05 2021

			The first  digit of the decimal expansion of Pi is 3, so a(1) = 1*3 = 3.
The second digit of the decimal expansion of Pi is 1, so a(2) = 2*1 = 2.
The third  digit of the decimal expansion of Pi is 4, so a(3) = 3*4 = 12.

Index entries for sequences related to the number Pi

Cf. A000796, A014976 (zeros), A053745 (fixed points).

Cf. A053746, A053747, A053748, A053749, A053750, A053751, A053752, A053753.

Module[{nn=120,pid},pid=RealDigits[Pi,10,nn][[1]];Table[n pid[[n]],{n,nn}]]

from sympy import S
def aupton(terms):
    digits_of_pi = "0" + str(S.Pi.n(terms+1)).replace('.', '')
    return [n*int(digits_of_pi[n]) for n in range(1, terms+1)]
print(aupton(59)) # Michael S. Branicky, Jul 08 2021

cp's OEIS Frontend

A037007 Positions of the digit '9' in the decimal expansion of Pi, where positions 0, 1, 2,... correspond to digits 3, 1, 4, ....

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A096567 First digit to appear n times in the base-10 expansion of Pi.

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A014976 Successive locations of zeros in decimal expansion of Pi (where locations 1, 2, 3, ... correspond to digits 3, 1, 4, ...).

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A053745 Positions of '1's in the decimal expansion of Pi (where positions 1,2,3,... refer to the digits 3,1,4,...).

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A053746 Positions of '2's in the decimal expansion of Pi, where positions 1, 2, 3, ... correspond to digits 3, 1, 4, ...

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A096566 a(n) = concatenation of 10 distinct decimal digits in order of n-th appearance in the base-10 expansion of Pi.

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A349551 Rectangular array with ten rows, read by falling antidiagonals: row k gives positions of k in the decimal expansion (A000796) of Pi.

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A108664 In the decimal expansion of Pi, lengths of sublists ending with 9.

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