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%I #28 Jul 10 2021 10:50:52
%S 49,100,144,169,361,400,441,900,1225,1369,1444,1600,1681,1936,2500,
%T 3249,3600,4225,4900,6400,8100,9025,9409,10000,10404,11025,11449,
%U 11664,12100,12544,14161,14400,14641,15625,16641,16900,19044,19600,22500,25600,28900
%N Squares which are a decimal concatenation of two or more squares.
%C 0 counts as a square here.
%D L. Widmer, Construction of Elements of the Smarandache Square-Partial-Digital Sequence, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 145-146.
%H Christian N. K. Anderson, <a href="/A019547/b019547.txt">Table of n, a(n) for n = 1..10000</a>
%H Christian N. K. Anderson, <a href="/A019547/a019547_1.txt">Table of n, a(n), sqrt(a(n)), all possible decompositions of a(n) into squares</a> for n = 1..10000 (excluding solutions with leading zeros)
%H Sylvester Smith, <a href="http://www.gallup.unm.edu/~smarandache/SYLSMITH.HTM">A Set of Conjectures on Smarandache Sequences</a>, Bulletin of Pure and Applied Sciences, (Bombay, India), Vol. 15 E (No. 1), 1996, pp. 101-107.
%F n^2 < a(n) < 100n^2. - _Charles R Greathouse IV_, Sep 19 2012
%F a(n) = A128783(n)^2. - _Michael S. Branicky_, Jul 10 2021
%e 1369 is a term as it can be partitioned as 1, 36 and 9. 1444 is a term as it can be partitioned as 1, 4, 4, 4. Again, 100 is 1, 0, 0.
%t r[n_, d_] := Catch@Block[{z = Length@d, t}, z < 1 || Do[If[IntegerQ@ Sqrt@ (t = FromDigits@Take[d, i]) && t < n && r[n, Take[d, i - z]], Throw@ True], {i, z}]]; Select[Range[4, 10^4]^2, r[#, IntegerDigits@ #] &] (* _Giovanni Resta_, Apr 30 2013 *)
%o (Python)
%o from math import isqrt
%o def issquare(n): return isqrt(n)**2 == n
%o def ok(n, c):
%o if n%10 in { 2, 3, 7, 8}: return False
%o if issquare(n) and c > 1: return True
%o d = str(n)
%o for i in range(1, len(d)):
%o if issquare(int(d[:i])) and ok(int(d[i:]), c+1): return True
%o return False
%o print([r*r for r in range(180) if ok(r*r, 1)]) # _Michael S. Branicky_, Jul 10 2021
%Y Cf. A010052, A000290, A128783.
%K nonn,base
%O 1,1
%A R. Muller
%E More terms from _Christian N. K. Anderson_, Apr 30 2013
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