A100322 a(n) is the smallest positive integer k such that the digits of the fractional part of Pi^k begin with n.

1, 7, 6, 4, 8, 23, 25, 2, 15, 91, 51, 307, 49, 1, 102, 315, 112, 12, 76, 26, 115, 208, 77, 276, 161, 40, 13, 41, 7, 99, 174, 169, 86, 453, 110, 204, 53, 6, 67, 4, 228, 123, 37, 134, 158, 192, 33, 45, 61, 200, 31, 324, 8, 56, 34, 105, 148, 17, 19, 92, 23, 38, 27, 39, 32, 82

Offset: 1

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 16 2004

Keywords

• base
• nonn

Examples

			Pi^1 = 3.14159..., whose digits after the decimal point begin with 1, so a(1)=1.
Pi^2 = 9.869..., whose digits after the decimal point begin with 8, so a(8)=2.
a(14)=1 because Pi^1 = 3.14....
		

Crossrefs

Cf. A000796, A002388, A091925, A092425, A092731, A092732, A092735, A092736.

Programs

PARI

a(n) = my(k=1); while (floor(frac(Pi^k)*10^(1+logint(n, 10))) != n, k++); k; \\ Michel Marcus, Jun 18 2022