A048375 Numbers whose square is a concatenation of two nonzero squares.

7, 13, 19, 35, 38, 41, 57, 65, 70, 125, 130, 190, 205, 223, 253, 285, 305, 350, 380, 410, 475, 487, 570, 650, 700, 721, 905, 975, 985, 1012, 1201, 1250, 1265, 1300, 1301, 1442, 1518, 1771, 1900, 2024, 2050, 2163, 2225, 2230, 2277, 2402, 2435, 2530, 2850

Offset: 1

Author

Patrick De Geest, Mar 15 1999

Keywords

• nonn
• easy
• nice
• base

Comments

Leading zeros not allowed, trailing zeros are.

This means that, e.g., 95 is not in the sequence although 95^2 = 9025 could be seen as concatenation of 9 and 025 = 5^2. - M. F. Hasler, Jan 25 2016

Examples

			1771^2 = 3136441 = 3136_441 and 3136 = 56^2, 441 = 21^2.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A039686, A048646.

Programs

Mathematica

squareQ[n_] := IntegerQ[Sqrt[n]]; okQ[n_] := MatchQ[IntegerDigits[n^2], {a__ /; squareQ[FromDigits[{a}]], b__ /; First[{b}] > 0 && squareQ[FromDigits[{b}]]}]; Select[Range[3000], okQ] (* Jean-François Alcover, Oct 20 2011, updated Dec 13 2016 *)

PARI

is_A048375(n)={my(p=100^valuation(n,10));n*=n;while(n>p*=10,issquare(n%p)&&issquare(n\p)&&n%p*10>=p&&return(1))} \\ M. F. Hasler, Jan 25 2016

Python

from math import isqrt
def issquare(n): return isqrt(n)**2 == n
def ok(n):
  d = str(n)
  for i in range(1, len(d)):
    if d[i] != '0' and issquare(int(d[:i])) and issquare(int(d[i:])):
      return True
  return False
print([r for r in range(2851) if ok(r*r)]) # Michael S. Branicky, Jul 13 2021

Formula

a(n) = sqrt(A039686(n)). - M. F. Hasler, Jan 25 2016