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

1,1

COMMENTS

It is very probable that a(n) = 2 for n > 169.

LINKS

Table of n, a(n) for n=1..80.

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

(Haskell)

import Data.List (isInfixOf)

a235052 n = head [x | x <- [2..], show x `isInfixOf` (show $ x ^ n)]

-- Reinhard Zumkeller, Jan 18 2014

CROSSREFS

Cf. 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

STATUS

approved

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Last modified September 20 01:28 EDT 2020. Contains 337238 sequences. (Running on oeis4.)