A037001 - OEIS

%I #25 Jul 29 2024 05:09:46

%S 6,16,21,28,33,53,63,73,76,83,89,93,102,112,114,135,136,140,149,160,

%T 165,173,185,186,203,221,229,241,244,260,275,280,289,292,298,302,326,

%U 329,333,335,337,354,374,380,406,423,435,456,462,477,479,484,485,500

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

%C 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

%H Amiram Eldar, <a href="/A037001/b037001.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PiDigits.html">Pi Digits.</a>

%H <a href="/index/Ph#Pi314">OEIS index to sequences related to Pi</a>.

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

%t Flatten @ Position[ RealDigits[Pi - 3, 10, 500][[1]], 2] (* _Robert G. Wilson v_, Mar 07 2011 *)

%o (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

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

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

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

%Y Cf. A035117 (first occurrence of at least n '1's), A050281 (n '2's), A050282, A050283, A050284, A050286, A050287, A048940 (n '9's).

%Y 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).

%Y Cf. A121280 = A068987 - 1: position of "123...n" in Pi's decimals.

%Y Cf. A176341: first occurrence of n in Pi's digits.

%K nonn,base

%O 1,1

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