A029942 Numbers k such that the decimal expansion of k^3 contains k as a substring.

0, 1, 4, 5, 6, 9, 10, 24, 25, 32, 40, 49, 50, 51, 56, 60, 75, 76, 90, 99, 100, 125, 240, 249, 250, 251, 375, 376, 400, 490, 499, 500, 501, 510, 600, 624, 625, 749, 750, 751, 760, 782, 875, 900, 990, 999, 1000, 1249, 1250, 2400, 2490, 2500, 2510

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base
• nice

Examples

			24 is a term as 24^3 = 13824 contains 24 as a substring.
250 is a term as 250^3 = 1562500 contains 250 as a substring.
6^3 = 21_6, 782^3 = 4_782_11768.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..1000 (first 500 terms from Reinhard Zumkeller)

Crossrefs

Cf. A018834 (squares), A075904 (4th powers), A075905 (5th powers), A136490 (base 2).

Cf. A000578. Supersequence of A029943.

Programs

Haskell

import Data.List (isInfixOf)
a029942 n = a029942_list !! (n-1)
a029942_list = [x | x <- [0..], show x `isInfixOf` show (x^3)]
-- Reinhard Zumkeller, Feb 29 2012

Mathematica

n3ssQ[n_]:=Module[{idn=IntegerDigits[n],idn3=Partition[ IntegerDigits[ n^3], IntegerLength[n],1]},MemberQ[idn3,idn]]; Join[{0},Select[Range[ 2600],n3ssQ]] (* Harvey P. Dale, Jan 23 2012 *)
Select[Range[0,2600],SequenceCount[IntegerDigits[#^3],IntegerDigits[ #]]> 0&] (* Harvey P. Dale, Aug 29 2021 *)