A235052 a(n) = smallest number > 1 such that a(n)^n contains a(n) as a substring.
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
Offset: 1
Examples
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.
Links
- Michael S. Branicky, Table of n, a(n) for n = 1..10000
Programs
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Haskell
import Data.List (isInfixOf) a235052 n = head [x | x <- [2..], show x `isInfixOf` (show $ x ^ n)] -- Reinhard Zumkeller, Jan 18 2014
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Mathematica
a[n_] := Block[{k = 2}, While[StringPosition[ToString[k^n], ToString@k] == {}, k++]; k]; Array[a, 80] (* Giovanni Resta, Jan 11 2014 *) -
PARI
a(n) = my(k=2); while(#strsplit(Str(k^n), Str(k))==1, k++); k; \\ Michel Marcus, Jan 25 2022
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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
Extensions
a(81) and beyond from Michael S. Branicky, Jan 25 2022
Comments