OFFSET
1,1
COMMENTS
Squares that can be split up in more than one way, e.g., 4950625 with sqrt(4 * 950625) = 1950 and sqrt(49 * 50625) = 1575, appear only once.
Squares that are members of this sequence in more than one way: 4950625, 495062500, 49506250000, 4950625000000, ..., . - Robert G. Wilson v, Aug 14 2015
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..1386 (first 200 terms from Reiner Moewald)
EXAMPLE
169 = 13^2 can be split up into 16 and 9 and 16*9 = 144, a square.
MAPLE
p:= proc(k, n) local t; t:= n mod 10^k; t >= 10^(k-1) and issqr(t*(n-t)/10^k) end proc:
filter:= n -> ormap(p, [$1..ilog10(n)], n):
select(filter, [seq(i^2, i=1..10^4)]); # Robert Israel, Sep 22 2015
MATHEMATICA
f[n_] := Block[{idn = IntegerDigits@ n, c = 0, k = 1, lmt = Floor[1 + Log10@ n]}, While[k < lmt, m = Mod[n, 10^(lmt - k)]; If[ IntegerQ@ Sqrt[ FromDigits[ Take[idn, {1, k}]] m] && m > 0 && IntegerDigits[m] == Take[idn, {k + 1, -1}], c++]; k++]; c]; Select[ Range[1700]^2, f@# > 0 &] (* Robert G. Wilson v, Aug 13 2015 *)
PROG
(Python)
import math
list =[]
for i in range(1, 100000):
...a = i*i
...b = str(a)
...l = len(b)
...for j in range(1, l):
......a_1 = b[:j]
......a_2 = b[j:]
......c = int(a_1)* int(a_2)
......sqrt_c = int(math.sqrt(int(c)))
......if (sqrt_c * sqrt_c == c) and (int(a_2[:1]) > 0):
.........if not a in list:
............list.append(a)
.........list.append(a)
print(list)
(PARI) isok(n) = {if (issquare(n), len = #Str(n); for (k=1, len-1, na = n\10^k; nb = n%10^k; if (na && nb && (eval(Str(na, nb))==n) && issquare(na*nb), return (1)); ); ); } \\ Michel Marcus, Oct 09 2015
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Reiner Moewald, Jul 26 2015
STATUS
approved