OFFSET
1,1
COMMENTS
0 counts as a square here.
REFERENCES
L. Widmer, Construction of Elements of the Smarandache Square-Partial-Digital Sequence, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997, 145-146.
LINKS
Christian N. K. Anderson, Table of n, a(n) for n = 1..10000
Christian N. K. Anderson, Table of n, a(n), sqrt(a(n)), all possible decompositions of a(n) into squares for n = 1..10000 (excluding solutions with leading zeros)
Sylvester Smith, A Set of Conjectures on Smarandache Sequences, Bulletin of Pure and Applied Sciences, (Bombay, India), Vol. 15 E (No. 1), 1996, pp. 101-107.
FORMULA
n^2 < a(n) < 100n^2. - Charles R Greathouse IV, Sep 19 2012
a(n) = A128783(n)^2. - Michael S. Branicky, Jul 10 2021
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(Python)
from math import isqrt
def issquare(n): return isqrt(n)**2 == n
def ok(n, c):
if n%10 in { 2, 3, 7, 8}: return False
if issquare(n) and c > 1: return True
d = str(n)
for i in range(1, len(d)):
if issquare(int(d[:i])) and ok(int(d[i:]), c+1): return True
return False
print([r*r for r in range(180) if ok(r*r, 1)]) # Michael S. Branicky, Jul 10 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
R. Muller
EXTENSIONS
More terms from Christian N. K. Anderson, Apr 30 2013
STATUS
approved