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

164, 1441, 1625, 1961, 2564, 4841, 12116, 14449, 16400, 25625, 46241, 48464, 115625, 116641, 144100, 148841, 160025, 162500, 163844, 169169, 184964, 193636, 196100, 256400, 361225, 368649, 466564, 484100, 493025, 961009, 973441, 1166464

Offset: 1

Author

Klaus Brockhaus and Zak Seidov, Jul 14 2011

Keywords

• nonn
• base

Comments

Subsequence of A191933.

If k is a term, then k followed by two zeros is also a term.

None of the terms < 40000000 is in more than two ways the concatenation of the decimal representation of two nonzero squares.

A038670 is a subsequence. - Reinhard Zumkeller, Jul 15 2011

Examples

			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.
		

Links

• Klaus Brockhaus, Table of n, a(n) for n = 1..100 (terms < 40000000)

Crossrefs

Cf. A000290, A191933.

Programs

Haskell

import Data.List (findIndices)
a192993 n = a192993_list !! (n-1)
a192993_list = findIndices (> 1) $ map a193095 [0..]
-- Reinhard Zumkeller, Jul 17 2011

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, []); 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 " : " */

Mathematica

f@n_ := DeleteDuplicates@
  Select[First@# & /@
    Select[Partition[
      Sort@(FromDigits@Flatten@IntegerDigits@# & /@
         Tuples[Range@Sqrt[10^(n - 1) - 1]^2, {2}]), 2, 1],
     Differences@# == {0} &], # <
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. *)