A014976 -id:A014976 - cp's OEIS frontend

A037008 Positions of the digit '0' in the decimal expansion of Pi, where positions 0, 1, 2, ... correspond to digits 3, 1, 4, ....

32, 50, 54, 65, 71, 77, 85, 97, 106, 116, 121, 128, 132, 146, 159, 164, 167, 176, 195, 207, 245, 248, 264, 270, 287, 291, 307, 308, 311, 327, 330, 340, 357, 360, 361, 366, 369, 375, 398, 403, 408, 421, 443, 451, 493, 513, 520, 523, 543, 545, 552, 557, 561

Offset: 1

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

			Pi = 3.14159 26535 89793 23846 26433 83279 5*0*288 4... (Position 32 refers to the 32nd digit after the decimal point.)

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.

Cf. A000796 (decimal expansion (or digits) of Pi).
For another version see A014976(n) = a(n) + 1.
For digits 0 through 9 see: this sequence, A037000, A037001, A037002, A037003, A037004, A037005, A036974, A037006, A037007.

Flatten @ Position[ RealDigits[Pi - 3, 10, 500][[1]], 0] (* Robert G. Wilson v, Mar 07 2011 *)

for(c=1,default(realprecision,2011)-2,Pi\.1^c%10 || print1(c",")) \\ M. F. Hasler, Oct 23 2011

A037008_upto(N=999)={localprec(N+20); [i-1|i<-[1..#N=digits(Pi\10^-N)],!N[i]]} \\ M. F. Hasler, Jul 29 2024

a(n) = A014976(n) - 1. - M. F. Hasler, Jul 29 2024

Name edited by 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

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

A088563 Primes p such that the p-th digit in the decimal expansion of Pi is 0.

Original entry on oeis.org

107, 271, 331, 367, 409, 521, 619, 683, 751, 839, 857, 997, 1013, 1117, 1123, 1361, 1439, 1483, 1489, 1601, 1607, 1609, 1747, 1831, 1889, 1913, 1999, 2131, 2137, 2251, 2341, 2671, 2819, 2887, 2957, 3011, 3019, 3169, 3203, 3253, 3299, 3331, 3407, 3413

Offset: 1

Cino Hilliard, Nov 19 2003

The 9th zero in Pi is in the 107th place of the digits 3,1,4,1,5, ...

Harvey P. Dale, Table of n, a(n) for n = 1..2000

Primes in A014976 (positions of '0's in decimal digits of Pi).

Cf. A088565 - A088566 (the same for digits 1 and 2), A000796 (decimal digits of Pi).

With[{pidigs=RealDigits[Pi,10,10000][[1]]},Select[Prime[ Range[ 500]], pidigs[[#]]==0&]] (* Harvey P. Dale, Nov 13 2011 *)

pizeros(n,d) = { default(realprecision,5000); p = Pi; v = Vec(Str(p)); for(x=1,n, if(v[x] == Str(d) && isprime(x-1),print1(x-1",")) ) }

A088563_upto(N=3456)={localprec(N+20); [p|p<-primes([1, #N=digits(Pi\10^-N)]), !N[p]]} \\ M. F. Hasler, Jul 29 2024

A088565 Primes p such that the p-th digit in the decimal expansion of Pi is 1.

Original entry on oeis.org

2, 41, 139, 149, 199, 239, 251, 397, 433, 439, 443, 491, 569, 599, 641, 647, 661, 787, 853, 883, 1031, 1087, 1097, 1153, 1187, 1319, 1423, 1613, 1619, 1637, 1657, 1667, 1697, 1759, 1789, 2081, 2129, 2143, 2221, 2239, 2459, 2633, 2689, 2741, 2753, 2777

Offset: 1

Cino Hilliard, Nov 19 2003

			The 1st digit 1 in Pi is in the 2nd place of the digits 3,1,4,1,5,9,..., and 2 is prime, whence a(1) = 2.  [Corrected and edited by _M. F. Hasler_, Jul 29 2024]

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Primes in A014976.

Cf. A088563, A088566 (the same for digits 0 and 2), A000796 (decimal digits of Pi).

Select[Flatten[Position[RealDigits[Pi,10,2800][[1]],1]],PrimeQ] (* Harvey P. Dale, May 05 2019 *)

pizeros(n,d) = { default(realprecision,5000); p = Pi; v = Vec(Str(p)); for(x=1,n, if(v[x] == Str(d) && isprime(x-1),print1(x-1",")) ) }

A088565_upto(N=3456, d=1)={localprec(N+20); [p|p<-primes([1, #N=digits(Pi\10^-N)]), N[p]==d]} \\ M. F. Hasler, Jul 29 2024

A014974 Differences between successive locations of zeros in decimal expansion of Pi.

Original entry on oeis.org

18, 4, 11, 6, 6, 8, 12, 9, 10, 5, 7, 4, 14, 13, 5, 3, 9, 19, 12, 38, 3, 16, 6, 17, 4, 16, 1, 3, 16, 3, 10, 17, 3, 1, 5, 3, 6, 23, 5, 5, 13, 22, 8, 42, 20, 7, 3, 20, 2, 7, 5, 4, 35, 5, 1, 1, 15, 20, 19, 2, 10, 13, 2, 19, 12, 5

Offset: 1

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

Assuming Pi is normal, this sequence includes every finite sequence of positive integers. - Franklin T. Adams-Watters, Mar 15 2006

			First two 0's are in 33rd and 51st digits, difference is 18.

Harvey P. Dale, Table of n, a(n) for n = 1..3000
Eric Weisstein's World of Mathematics, Normal Number.

Cf. A000796, A037008, A139728, A108664.

Differences[Flatten[Position[RealDigits[Pi,10,1000][[1]],0]]] (* Harvey P. Dale, Jul 04 2017 *)

a(n) = A014976(n+1) - A014976(n). - Michel Marcus, Oct 06 2013

More terms from Simon Plouffe.

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 *)

A256109 Index of the n-th zero in the first occurrence of a string of exactly n zeros in the decimal expansion of Pi.

Original entry on oeis.org

33, 309, 604, 13394, 17539, 1699933, 3794579, 172330858, 2542542111, 8324296445, 371247087583, 1755524129985, 3186699229903, 6381820482345

Offset: 1

Kival Ngaokrajang, Mar 14 2015

a(n) is the least k such that A000796(k-n+1) = ... = A000796(k) = 0 and A000796(k+1) != 0. - Danny Rorabaugh, Mar 31 2015

Dave Andersen, The Pi-Search Page.

Cf. A000796, A050279, A014976, A256160.

{ default(realprecision, 20080); for (m = 1, 10, x = Pi; r = 0; for (n = 1, 20000, d = floor(x); x = (x-d)*10; if(d <> 0, if (r <> m, r = 0, print1(n-1, ", "); r = 0; break), r = r + 1)))}

a(n) = A050279(n) + n. - Danny Rorabaugh, Mar 31 2015

a(6)-a(10) by Danny Rorabaugh, Mar 31 2015

a(11)-a(14) added using A050279 by Jinyuan Wang, Mar 30 2020

A329368 Partition the decimal expansion of Pi into non-overlapping strings of length 10: 3141592653, 5897932384,..; a(n) is the position of the strings where digits are different from each other.

Original entry on oeis.org

7, 548, 3113, 11665, 11728, 14305, 15762, 19177, 23288, 28259, 35603, 37613, 40595, 40740, 41477, 52108, 54085, 54367, 62272, 74856, 75082, 75178, 82919, 83591, 92284, 94936, 103849, 105419, 105832, 108875, 111962, 115152, 117919, 118976, 121112, 124121, 128505

Offset: 1

XU Pingya, Apr 27 2020

			a(1) = 7, because such a string first occur at the 7th string: 4592307816 (i.e., 61-70 digits of Pi).

David Blatner, The Joy of Pi, Walker and Co., NY, 1997; page 91.

Eric Weisstein's World of Mathematics, Pi Digits

Cf. A000796, A014976, A050278, A096760, A101815, A101816, A107115.

q[i_]:=q[i]=Take[RealDigits[Pi,10,10i][[1]],-10];
a={}; Do[If[Length@Union@q[i]==10, AppendTo[a,i]], {i,130000}]
a

cp's OEIS Frontend

A037008 Positions of the digit '0' 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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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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A088563 Primes p such that the p-th digit in the decimal expansion of Pi is 0.

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A088565 Primes p such that the p-th digit in the decimal expansion of Pi is 1.

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A014974 Differences between successive locations of zeros in decimal expansion of Pi.

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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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