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

1,1

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.

Sequence in context: A122482 A265629 A283191 * A198035 A208720 A208776

Adjacent sequences: A048372 A048373 A048374 * A048376 A048377 A048378

Keyword

nonn,easy,nice,base

Author

Patrick De Geest, Mar 15 1999

Status

approved