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A051248
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n^a(n) is the smallest power of n (with a(n) > 1) which starts with n.
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10
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2, 8, 18, 6, 24, 10, 20, 11, 22, 2, 26, 14, 10, 8, 92, 6, 166, 5, 19, 11, 60, 39, 48, 51, 94, 42, 467, 86, 14, 66, 58, 3, 5268, 33, 58, 10, 45, 70, 23, 6, 205, 70, 31, 15, 50, 84, 248, 70, 72, 94, 107, 170, 30, 10139, 182, 136, 87, 318, 49, 10, 178, 237, 295, 99, 17, 206
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OFFSET
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1,1
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COMMENTS
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The largest of the first 10000 terms is a(1955) = 119589011. - Giovanni Resta, May 27 2016
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LINKS
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EXAMPLE
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2^8 = 256 begins with 2, and 2^k does not begin with 2 for any smaller integer k > 1, so a(2) = 8.
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MATHEMATICA
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f[n_]:=Module[{i=2}, While[Take[IntegerDigits[n^i], IntegerLength[n]] != IntegerDigits[n], i++]; i]; Array[f, 70] (* Harvey P. Dale, Oct 04 2011 *)
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PROG
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(Haskell)
import Data.List (isPrefixOf)
a051248 n = 2 + length
(takeWhile (not . (show n `isPrefixOf`) . show) $ iterate (* n) (n^2))
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CROSSREFS
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KEYWORD
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nonn,base,nice
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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