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

1,3

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

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

Cf. A000578. Supersequence of A029943.

Sequence in context: A082812 A255634 A075903 * A162016 A242040 A206822

Adjacent sequences: A029939 A029940 A029941 * A029943 A029944 A029945

Keyword

nonn,base,nice

Author

Patrick De Geest

Status

approved