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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified June 12 14:32 EDT 2021. Contains 344957 sequences. (Running on oeis4.)