A048375 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

LINKS

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

FORMULA

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

EXAMPLE

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

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 *)

PROG

(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

CROSSREFS

Cf. A039686, A048646.