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A100322
a(n) is the smallest positive integer k such that the digits of the fractional part of Pi^k begin with n.
3
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
1,2
EXAMPLE
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....
PROG
(PARI) a(n) = my(k=1); while (floor(frac(Pi^k)*10^(1+logint(n, 10))) != n, k++); k; \\ Michel Marcus, Jun 18 2022
KEYWORD
base,nonn
AUTHOR
Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 16 2004
STATUS
approved