

A239134


Smallest k such that n^k contains k as a substring in its decimal representation.


1



1, 6, 7, 6, 2, 6, 3, 4, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 6, 1, 4, 2, 3, 2, 4, 2, 4, 3, 7, 1, 2, 3, 3, 2, 2, 3, 5, 2, 6, 1, 8, 4, 4, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 4, 2, 4, 3, 6, 1, 3, 5, 6, 2, 4, 3, 2, 3, 3, 1, 3, 2, 6, 2, 3, 2, 6, 2, 4, 1, 2, 4, 4
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OFFSET

1,2


COMMENTS

Is it very likely a(n) < 10 for all n (even stronger, a(n) < 9 for all n).
Is it also very likely a(n) = {1,2,3} for sufficiently large n.


LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000


FORMULA

a(A011531(k))=1, any k.


EXAMPLE

5^1 = 5 does not contain a 1 but 5^2 = 25 does contain a 2 so a(5) = 2.
7^1 = 7 does not contain a 1, 7^2 = 49 does not contain a 2, but 7^3 = 343 does contain a 3 so a(7) = 3.


MATHEMATICA

a[n_] := Block[{k=1}, While[{} == StringPosition[ ToString[n^k], ToString[k]], k++]; k]; Array[a, 84] (* Giovanni Resta, Mar 11 2014 *)


PROG

(Python)
def Sub(x):
..for n in range(10**3):
....if str(x**n).find(str(n)) > 1:
......return n
x = 1
while x < 10**3:
..print(Sub(x))
..x += 1


CROSSREFS

Cf. A061280.
Sequence in context: A321094 A330114 A011423 * A196616 A253271 A258945
Adjacent sequences: A239131 A239132 A239133 * A239135 A239136 A239137


KEYWORD

nonn,base


AUTHOR

Derek Orr, Mar 10 2014


STATUS

approved



