A037000 Positions of the digit '1' in the decimal expansion of Pi.

1, 3, 37, 40, 49, 68, 94, 95, 103, 110, 138, 148, 153, 154, 155, 163, 168, 174, 175, 198, 206, 220, 238, 243, 246, 250, 269, 281, 295, 297, 314, 319, 324, 342, 344, 362, 363, 381, 385, 390, 393, 395, 396, 417, 424, 427, 428, 432, 437, 438, 442, 445, 446

Offset: 1

Author

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

Keywords

• base
• nonn

Comments

From M. F. Hasler, Jul 28 2024: (Start)

"Positions" are indices n of digits d(n) such that Pi = Sum_{n >= 0} d(n)/10^n; see A053745 for the variant where the initial digit 3 is at position 1.

The first few primes in this sequence are 3, 37, 103, 163, 269, 281, 499, 541, 547, 587, 607, 709, 797, 859, 887, 971, 983, 997, ... (End)

Links

• Robert Israel, Table of n, a(n) for n = 1..10137
• Eric Weisstein's World of Mathematics, Pi Digits

Crossrefs

Cf. A000796 (decimals of Pi), A037001 - A037008 and A036974 (positions of other digits), A053745 (variant with all values increased by 1).

Programs

Maple

P:= convert(evalf[100000](Pi),string)[3..-1]:
select(t -> P[t]="1",[$1..length(P)-1]); # Robert Israel, Dec 22 2013

Mathematica

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

PARI

A037000_upto(N=500, d=1)={localprec(N+20); [i-1|i<-[1..#N=digits(Pi\10^-N)], N[i]==d]} \\ M. F. Hasler, Jul 28 2024

Formula

Conjecturally, a(n) ~ 10n.