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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 *) sk[n_]:=Module[{k=1}, While[SequenceCount[IntegerDigits[n^k], IntegerDigits[k]] == 0, k++]; k]; Array[sk, 90] (* Harvey P. Dale, May 12 2022 *) 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 August 15 20:27 EDT 2022. Contains 356148 sequences. (Running on oeis4.)