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

1,2

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

Formula

Conjecturally, a(n) ~ 10n.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A128061 A176240 A116184 * A042333 A106103 A224471

Adjacent sequences: A036997 A036998 A036999 * A037001 A037002 A037003

Keyword

base,nonn

Author

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

Status

approved