A037001 Positions of the digit '2' in the decimal expansion of Pi (where positions 0, 1, 2,... refer to the digits 3, 1, 4,...).

6, 16, 21, 28, 33, 53, 63, 73, 76, 83, 89, 93, 102, 112, 114, 135, 136, 140, 149, 160, 165, 173, 185, 186, 203, 221, 229, 241, 244, 260, 275, 280, 289, 292, 298, 302, 326, 329, 333, 335, 337, 354, 374, 380, 406, 423, 435, 456, 462, 477, 479, 484, 485, 500

Offset: 1

Author

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

Keywords

• nonn
• base

Comments

The first few primes in this sequence are 53, 73, 83, 89, 149, 173, 229, 241, 337, 479, 571, 613, 661, 757, 829, 877, 911, 977, 991, ... - M. F. Hasler, Jul 28 2024

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Pi Digits.
• OEIS index to sequences related to Pi.

Crossrefs

Cf. A000796 (decimal expansion (or digits) of Pi).

Cf. A053746 (= a(n) + 1: the same with different offset).

Cf. A037000, A037002, A037003, A037004, A037005, A036974, A037006, A037007, A037008 (similar for digits 1, ..., 9 and 0).

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.

Programs

Mathematica

Flatten @ Position[ RealDigits[Pi - 3, 10, 500][[1]], 2] (* Robert G. Wilson v, Mar 07 2011 *)

PARI

A037001_upto(N=999, d=2)={localprec(N+20); [i-1|i<-[1..#N=digits(Pi\10^-N)], N[i]==d]} \\ M. F. Hasler, Jul 28 2024

Formula

a(n) ~ 10*n if Pi is normal, as generally assumed. - M. F. Hasler, Jul 28 2024