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 A235052 a(n) = smallest number > 1 such that a(n)^n contains a(n) as a substring. 2
 2, 5, 4, 5, 2, 4, 2, 2, 2, 2, 2, 3, 2, 4, 2, 3, 2, 2, 2, 3, 2, 3, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 4, 3, 3, 2, 2, 3, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It is very probable that a(n) = 2 for n > 169. a(n) <= 5 since 5^n ends in 5 for n > 0. - Michael S. Branicky, Jan 25 2022 LINKS Michael S. Branicky, Table of n, a(n) for n = 1..10000 EXAMPLE 4 is the smallest number such that 4^3 contains a 4 and 4^6 contains a 4, so a(3) = 4 and a(6) = 4. MATHEMATICA a[n_] := Block[{k = 2}, While[StringPosition[ToString[k^n], ToString@k] == {}, k++]; k]; Array[a, 80] (* Giovanni Resta, Jan 11 2014 *) PROG (Python) def f(x): for n in range(2, 10**3): if str(n**x).count(str(n)) > 0: return n x = 1 while x < 200: print(f(x)) x += 1 (Python) def a(n): return min(k for k in range(2, 6) if str(k) in str(k**n)) print([a(n) for n in range(1, 88)]) # Michael S. Branicky, Jan 25 2022 (Haskell) import Data.List (isInfixOf) a235052 n = head [x | x <- [2..], show x `isInfixOf` (show \$ x ^ n)] -- Reinhard Zumkeller, Jan 18 2014 (PARI) a(n) = my(k=2); while(#strsplit(Str(k^n), Str(k))==1, k++); k; \\ Michel Marcus, Jan 25 2022 CROSSREFS Cf. A034293, A236046. Sequence in context: A095758 A299212 A249018 * A102066 A279404 A072970 Adjacent sequences: A235049 A235050 A235051 * A235053 A235054 A235055 KEYWORD nonn,base AUTHOR Derek Orr, Jan 02 2014 EXTENSIONS a(81) and beyond from Michael S. Branicky, Jan 25 2022 STATUS approved

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Last modified September 23 10:17 EDT 2023. Contains 365544 sequences. (Running on oeis4.)