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

Author

Patrick De Geest

Keywords

• nonn
• base
• nice

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

Programs

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

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 *)

Formula

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

Extensions

Offset corrected by Reinhard Zumkeller, Nov 26 2011