A029943 Substring of both its square and its cube.

0, 1, 5, 6, 10, 25, 50, 60, 76, 100, 250, 376, 500, 600, 625, 760, 1000, 2500, 3760, 5000, 6000, 6250, 7600, 9376, 10000, 25000, 37600, 50000, 60000, 62500, 76000, 90625, 93760, 100000, 109376, 250000, 376000, 500000, 600000, 625000

Offset

1,3

Comments

Intersection of A018834 and A029942. - Reinhard Zumkeller, Feb 29 2012

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..100

Eric Weisstein's World of Mathematics, Automorphic Number

Wikipedia, Automorphic number

Index entries for sequences related to automorphic numbers

Formula

a(n) = A003226(m) * 10^k for appropriate m and k. [Reinhard Zumkeller, Nov 26 2011]

Mathematica

ssscQ[n_]:=Module[{idn=IntegerDigits[n], sq=IntegerDigits[n^2], cu=IntegerDigits[n^3], len=IntegerLength[n]}, MemberQ[Partition[ sq, len, 1], idn] &&MemberQ[Partition[cu, len, 1], idn]]; Join[{0}, Select[Range[700000], ssscQ]] (* Harvey P. Dale, Apr 24 2011 *)

Prog

(Haskell)
import Data.List (isInfixOf)
a029943 n = a029943_list !! (n-1)
a029943_list = filter f [0..] where
   f x = show x `isInfixOf` show (x^2) && show x `isInfixOf` show (x^3)
-- Reinhard Zumkeller, Nov 26 2011

Crossrefs

Sequence in context: A075156 A075904 A018834 * A356760 A063630 A342127

Adjacent sequences: A029940 A029941 A029942 * A029944 A029945 A029946

Keyword

nonn,base,nice

Author

Patrick De Geest

Extensions

Offset corrected by Reinhard Zumkeller, Nov 26 2011

Status

approved