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

1,1

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

Links

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

Example

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.

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. *)

Prog

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

Crossrefs

Cf. A000290, A191933.

Sequence in context: A223455 A251197 A038670 * A250935 A250928 A205314

Adjacent sequences: A192990 A192991 A192992 * A192994 A192995 A192996

Keyword

nonn,base

Author

Klaus Brockhaus and Zak Seidov, Jul 14 2011

Status

approved