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

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
(Python)
def a(n):
    k, sk = 1, str(n)
    while len(set(sk)) == len(sk): k += 1; sk = str(n**k)
    return k
print([a(n) for n in range(2, 102)]) # Michael S. Branicky, Jul 23 2022

Crossrefs

Cf. A337241 (similar for k*n instead of n^k).

Sequence in context: A007263 A033336 A204325 * A102270 A102272 A304227

Adjacent sequences: A355870 A355871 A355872 * A355874 A355875 A355876

Keyword

nonn,easy,base

Author

Steven Haye Nicolaij, Jul 19 2022

Status

approved