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A018834 Numbers k such that the decimal expansion of k^2 contains k as a substring.

%I A018834 #49 Apr 04 2024 10:08:24
%S A018834 0,1,5,6,10,25,50,60,76,100,250,376,500,600,625,760,1000,2500,3760,
%T A018834 3792,5000,6000,6250,7600,9376,10000,14651,25000,37600,50000,60000,
%U A018834 62500,76000,90625,93760,100000,109376,250000,376000,495475,500000,505025
%N A018834 Numbers k such that the decimal expansion of k^2 contains k as a substring.
%H A018834 Giovanni Resta, <a href="/A018834/b018834.txt">Table of n, a(n) for n = 1..200</a> (first 126 terms from David W. Wilson)
%e A018834 25^2 = 625 which contains 25.
%e A018834 3792^2 = 14_3792_64, 14651^2 = 2_14651_801.
%t A018834 Select[Range[510000], MemberQ[FromDigits /@ Partition[IntegerDigits[#^2], IntegerLength[#], 1], #] &] (* _Jayanta Basu_, Jun 29 2013 *)
%t A018834 Select[Range[0,510000],StringPosition[ToString[#^2],ToString[#]]!={}&] (* _Ivan N. Ianakiev_, Oct 02 2016 *)
%o A018834 (Haskell)
%o A018834 import Data.List (isInfixOf)
%o A018834 a018834 n = a018834_list !! (n-1)
%o A018834 a018834_list = filter (\x -> show x `isInfixOf` show (x^2)) [0..]
%o A018834 -- _Reinhard Zumkeller_, Jul 27 2011
%o A018834 (Python)
%o A018834 from itertools import count, islice
%o A018834 def A018834_gen(startvalue=0): # generator of terms >= startvalue
%o A018834     return filter(lambda n:str(n) in str(n**2), count(max(startvalue,0)))
%o A018834 A018834_list = list(islice(A018834_gen(),20)) # _Chai Wah Wu_, Apr 04 2023
%Y A018834 Cf. A003226, A046831, A046851, A045953.
%Y A018834 Cf. A000290. Supersequence of A029943.
%Y A018834 Cf. A018826 (base 2), A018827 (base 3), A018828 (base 4), A018829 (base 5), A018830 (base 6), A018831 (base 7), A018832 (base 8), A018833 (base 9).
%Y A018834 Cf. A029942 (cubes), A075904 (4th powers), A075905 (5th powers).
%K A018834 nonn,base
%O A018834 1,3
%A A018834 _David W. Wilson_