A355873 - OEIS

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A355873

a(n) is the smallest positive exponent k such that the decimal expansion of n^k has at least one digit that occurs more than once.

16, 8, 8, 6, 5, 3, 6, 4, 2, 1, 2, 5, 3, 2, 4, 5, 5, 4, 2, 2, 1, 3, 4, 3, 2, 4, 3, 4, 2, 3, 5, 1, 2, 2, 3, 3, 2, 2, 2, 2, 3, 3, 1, 2, 2, 2, 3, 3, 2, 3, 3, 3, 3, 1, 2, 3, 2, 4, 2, 3, 2, 2, 3, 2, 1, 2, 2, 4, 2, 3, 3, 4, 3, 2, 2, 1, 3, 3, 2, 2, 3, 2, 4, 2, 3, 3, 1, 3, 2, 2, 2, 4, 2, 3, 3, 2, 3, 1, 1, 1

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OFFSET

2,1

LINKS

Table of n, a(n) for n=2..101.

Index entries for linear recurrences with constant coefficients, signature (1).

FORMULA

a(n) = 1 for all n > 9876543210.

EXAMPLE

a(9) = 4 because 9^4 = 6561 has two digits 6 and 9^1 = 9, 9^2 = 81, 9^3 = 729, all with distinct digits.

PROG

(PARI) a(n) = my(d=digits(n), k=1); while(#d == #Set(d), k++; d=digits(n^k)); k; \\ Michel Marcus, Jul 20 2022