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

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

Author

Simon Plouffe, Feb 20 2000

Keywords

• nonn
• base

Links

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

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