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 1-4 of 4 results.

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

Views

Author

Simon Plouffe, Feb 20 2000

Keywords

Links

Crossrefs

Cf. A014976, A053746 - A053753 (the same for digits 0, ..., 9).
Cf. A088565 (primes in this sequence), A000796 (decimal digits of Pi).

Programs

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

Formula

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

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

A088566 Primes p such that the p-th digit in the decimal expansion of Pi is 2.

Original entry on oeis.org

7, 17, 29, 103, 113, 137, 281, 293, 457, 463, 547, 601, 631, 823, 1051, 1091, 1109, 1201, 1231, 1283, 1301, 1327, 1399, 1427, 1447, 1487, 1523, 1621, 1663, 1733, 1847, 1907, 1949, 2099, 2141, 2281, 2297, 2309, 2377, 2767, 3023, 3037, 3119, 3121, 3391, 3457
Offset: 1

Views

Author

Cino Hilliard, Nov 19 2003

Keywords

Examples

			In the decimal digits of Pi = 3.14159265... the first 2 occurs as the 7th digit, and 7 is prime; therefore a(1) = 7.

Crossrefs

Primes in A053746.
Cf. A088563 (similar for digits 0), A088565 (for digits 1),
Cf. A000796 (decimal digits of Pi).

Programs

  • 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
    A088566_upto(N=3456, d=2)={localprec(N+20); [p|p<-primes([1, #N=digits(Pi\10^-N)]), N[p]==d]} \\ M. F. Hasler, Jul 28 2024

A373471 Primes indices of nonzero bits in Pi (A256108).

Original entry on oeis.org

3, 11, 13, 19, 23, 29, 41, 43, 47, 53, 71, 103, 107, 131, 149, 163, 173, 179, 197, 211, 227, 229, 239, 269, 281, 283, 293, 311, 349, 373, 379, 397, 409, 421, 457, 541, 557, 563, 577, 587, 599, 601, 607, 613, 617, 643, 647, 653, 659, 673, 709, 727, 733, 739, 743
Offset: 1

Views

Author

M. F. Hasler, Jul 27 2024

Keywords

Comments

Base 2 analog of A088565 (prime positions of '1's in decimal digits of Pi).

Examples

			Written in binary, Pi = 11.0010010000111111011010101000100010...[2] = Sum_{n >= -1} 2^-A256108(n), so the bits 1 have positions (-1, 0, 3, 6, 11, 12, 13, 14, 15, 16, 18, 19, 21, 23, 25, 29, 33, ...) and primes in this sequence are (3, 11, 13, 19, 23, ...) = this sequence.

Links

Crossrefs

Cf. A256108 (indices of nonzero bits in Pi), A004601 (Pi in base 2), A051480 (run lengths in A004601).
Cf. A088563 (indices of '0's in decimals of Pi).
Cf. A088565 (prime indices of '1's in the decimal digits of Pi).

Programs

  • Mathematica
    Select[PositionIndex[First[RealDigits[Pi, 2, 1000]]][1] - 2, PrimeQ] (* Paolo Xausa, Jul 31 2024 *)
  • PARI
    select(isprime, A256108_upto(777))
Showing 1-4 of 4 results.

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