cp's OEIS Frontend

A014563 a(n+1) is the smallest number > a(n) such that the digits of a(n)^2 are all (with multiplicity) contained in the digits of a(n+1)^2, with a(0)=1.

%I A014563 #25 Mar 06 2017 15:24:27
%S A014563 1,4,13,14,31,36,54,96,113,311,487,854,1036,1277,1646,3214,8351,10456,
%T A014563 11414,11536,11563,17606,17813,30287,36786,41544,54927,56547,56586,
%U A014563 57363,62469,62634,72813,72897,76944,78345,95061,97944,100963,101944
%N A014563 a(n+1) is the smallest number > a(n) such that the digits of a(n)^2 are all (with multiplicity) contained in the digits of a(n+1)^2, with a(0)=1.
%C A014563 Probably infinite. - _David W. Wilson_, Jan 29 2002
%H A014563 Reinhard Zumkeller, <a href="/A014563/b014563.txt">Table of n, a(n) for n = 0..1000</a>
%e A014563 13^2 = 169 and 14 is the next smallest number whose square (in this case 196) contains the digits 1,6,9.
%t A014563 snd[n_]:=Module[{k=n+1},While[!AllTrue[Select[Transpose[{DigitCount[n^2],
%t A014563 DigitCount[k^2]}],#[[1]]>0&],#[[1]]<=#[[2]]&],k++];k]; NestList[ snd,1,40] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Sep 21 2016 *)
%o A014563 (Haskell)
%o A014563 import Data.List ((\\))
%o A014563 a014563 n = a014563_list !! n
%o A014563 a014563_list = 1 : f 1 (drop 2 a000290_list) where
%o A014563    f x (q:qs) | null $ xs \\ (show q) = y : f y qs
%o A014563               | otherwise             = f x qs
%o A014563               where y = a000196 q; xs = show (x * x)
%o A014563 -- _Reinhard Zumkeller_, Nov 22 2012
%Y A014563 If "contained in" is replaced by "properly contained in" we get A065297.
%Y A014563 Cf. A066825, A067633, A067634, A067635, A065297.
%Y A014563 Cf. A000290, A000196.
%K A014563 base,nonn,nice
%O A014563 0,2
%A A014563 _Marc Paulhus_, Jan 29 2002