A037007 Positions of the digit '9' in the decimal expansion of Pi, where positions 0, 1, 2,... correspond to digits 3, 1, 4, ....

5, 12, 14, 30, 38, 42, 44, 45, 55, 58, 62, 79, 80, 100, 122, 129, 144, 169, 180, 187, 190, 193, 199, 208, 214, 247, 249, 259, 284, 294, 328, 331, 336, 341, 353, 356, 388, 391, 399, 414, 416, 418, 422, 433, 440, 459, 460, 465, 482, 487, 496, 498, 501, 527

Offset

1,1

Comments

Primes in this sequence are 5, 79, 193, 199, 331, 353, 433, 487, 941, ... - M. F. Hasler, Jul 29 2024

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..369 from M. F. Hasler)

Eric Weisstein's World of Mathematics, Pi Digits.

Index entries for sequences related to the number Pi

Formula

a(n) = A053753(n) - 1. - 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

Example

The first digit '9' occurs in 3.1415926... at the 5th place after the decimal point, whence a(1) = 5.

Mathematica

Flatten @ Position[ RealDigits[Pi - 3, 10, 500][[1]], 9] (* Robert G. Wilson v, Mar 07 2011 *)

Prog

(PARI) A037007_upto(N=999, d=9)={localprec(N+20); [i-1|i<-[1..#N=digits(Pi\10^-N)], N[i]==d]} \\ M. F. Hasler, Jul 29 2024

Crossrefs

Cf. A000796 (decimals of Pi).

Cf. A053753 (variant with all values increased by 1).

Cf. A037000, A037001, A037002, A037003, A037004, A037005, A036974, A037006, A037008 (similar for digits 1, ..., 8 and 0).

Cf. A048940, A096763 (starting position of at least/exactly n '9's).

Sequence in context: A286242 A360137 A185871 * A357999 A066025 A009824

Adjacent sequences: A037004 A037005 A037006 * A037008 A037009 A037010

Keyword

nonn,base

Author

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

Status

approved