cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Views

Author

Simon Plouffe, Feb 20 2000

Keywords

Comments

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

Examples

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

Links

Crossrefs

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).

Programs

  • Mathematica
    Flatten[Position[RealDigits[Pi, 10, 1000][[1]], 2]] (* Vincenzo Librandi, Oct 07 2013 *)
  • PARI
    A053746_upto(N=999)={localprec(N+20); select(d->d==2, digits(Pi\10^-N), 1)} \\ M. F. Hasler, Jul 28 2024

Formula

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

Extensions

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

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

Views

Author

Cino Hilliard, Nov 19 2003

Keywords

Comments

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

Links

Crossrefs

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).

Programs

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

Views

Author

Cino Hilliard, Nov 19 2003

Keywords

Examples

			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]

Links

Crossrefs

Primes in A014976.
Cf. A088563, A088566 (the same for digits 0 and 2), A000796 (decimal digits of Pi).

Programs

  • Mathematica
    Select[Flatten[Position[RealDigits[Pi,10,2800][[1]],1]],PrimeQ] (* Harvey P. Dale, May 05 2019 *)
  • PARI
    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",")) ) }
  • PARI
    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
Showing 1-3 of 3 results.

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