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A192993 Numbers that are in more than one way the concatenation of the decimal representation of two nonzero squares.

%I A192993 #22 Jul 15 2023 06:27:37
%S A192993 164,1441,1625,1961,2564,4841,12116,14449,16400,25625,46241,48464,
%T A192993 115625,116641,144100,148841,160025,162500,163844,169169,184964,
%U A192993 193636,196100,256400,361225,368649,466564,484100,493025,961009,973441,1166464
%N A192993 Numbers that are in more than one way the concatenation of the decimal representation of two nonzero squares.
%C A192993 Subsequence of A191933.
%C A192993 If k is a term, then k followed by two zeros is also a term.
%C A192993 None of the terms < 40000000 is in more than two ways the concatenation of the decimal representation of two nonzero squares.
%C A192993 A038670 is a subsequence. - _Reinhard Zumkeller_, Jul 15 2011
%H A192993 Klaus Brockhaus, <a href="/A192993/b192993.txt">Table of n, a(n) for n = 1..100</a> (terms < 40000000)
%e A192993 2564 is the concatenation of 256 and 4 as well as of 25 and 64; 256, 4, 25, 64 are squares, so 2564 is a term.
%t A192993 f@n_ := DeleteDuplicates@
%t A192993   Select[First@# & /@
%t A192993     Select[Partition[
%t A192993       Sort@(FromDigits@Flatten@IntegerDigits@# & /@
%t A192993          Tuples[Range@Sqrt[10^(n - 1) - 1]^2, {2}]), 2, 1],
%t A192993      Differences@# == {0} &], # <
%t A192993 10^n &]; f@7 (* _Hans Rudolf Widmer_, Jun 12 2023 *) (* Numbers with at most n digits that are in more than one way the concatenation of the decimal representation of two nonzero squares. *)
%o A192993 (Magma) SplitToSquares:=function(n); V:=[]; S:=Intseq(n); for j in [1..#S-1] do A:=[ S[k]: k in [1..j] ]; a:=Seqint(A); B:=[ S[k]: k in [j+1..#S] ]; b:=Seqint(B); if a gt 0 and A[#A] gt 0 and IsSquare(a) and IsSquare(b) then Append(~V, [<b, a>]); end if; end for; return V; end function; [ p: p in [1..1200000] | #P gt 1 where P is SplitToSquares(p) ]; /* to obtain the splittings replace " p: " with " <p, P>: " */
%o A192993 (Haskell)
%o A192993 import Data.List (findIndices)
%o A192993 a192993 n = a192993_list !! (n-1)
%o A192993 a192993_list = findIndices (> 1) $ map a193095 [0..]
%o A192993 -- _Reinhard Zumkeller_, Jul 17 2011
%Y A192993 Cf. A000290, A191933.
%K A192993 nonn,base
%O A192993 1,1
%A A192993 _Klaus Brockhaus_ and _Zak Seidov_, Jul 14 2011