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Substring of both its square and its cube.
6

%I #33 Feb 18 2024 02:04:18

%S 0,1,5,6,10,25,50,60,76,100,250,376,500,600,625,760,1000,2500,3760,

%T 5000,6000,6250,7600,9376,10000,25000,37600,50000,60000,62500,76000,

%U 90625,93760,100000,109376,250000,376000,500000,600000,625000

%N Substring of both its square and its cube.

%C Intersection of A018834 and A029942. - _Reinhard Zumkeller_, Feb 29 2012

%H Reinhard Zumkeller, <a href="/A029943/b029943.txt">Table of n, a(n) for n = 1..100</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/AutomorphicNumber.html">Automorphic Number</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Automorphic_number">Automorphic number</a>

%H <a href="/index/Ar#automorphic">Index entries for sequences related to automorphic numbers</a>

%F a(n) = A003226(m) * 10^k for appropriate m and k. [_Reinhard Zumkeller_, Nov 26 2011]

%t 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 *)

%o (Haskell)

%o import Data.List (isInfixOf)

%o a029943 n = a029943_list !! (n-1)

%o a029943_list = filter f [0..] where

%o f x = show x `isInfixOf` show (x^2) && show x `isInfixOf` show (x^3)

%o -- _Reinhard Zumkeller_, Nov 26 2011

%K nonn,base,nice

%O 1,3

%A _Patrick De Geest_

%E Offset corrected by _Reinhard Zumkeller_, Nov 26 2011