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

Author

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

Keywords

• nonn
• base

Comments

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

Examples

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

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

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).

Programs

Mathematica

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

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

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