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
KEYWORD
nonn,base
AUTHOR
Klaus Brockhaus and Zak Seidov, Jul 14 2011
STATUS
approved