A239975 - OEIS

%I #16 Mar 21 2022 11:11:23

%S 7,2,17,7,3,14,49,4,71,34,5,14,127,6,161,1,7,98,241,8,35,142,9,17,391,

%T 10,449,28,11,254,49,12,647,322,13,2,799,14,881,73,15,482,1057,7,119,

%U 70,17,113,1351,18,77,34,19,782,1681,3,1799,898,21,56,7,22,2177,217,23

%N Least k>0 such that n^2 + (n+k)^2 is a square, or -1 if no such k exists.

%C a(3*n) <= n because with k=n: (3*n)^2 + (4*n)^2 = (5*n)^2.

%H Michael S. Branicky, <a href="/A239975/b239975.txt">Table of n, a(n) for n = 5..10004</a>

%e a(6) = 2 because 6^2 + (6+2)^2 = 100 is a square.

%e a(20) = 1 because 20^2 + 21^2 = 841 = 29^2.

%o (PARI) s=[]; for(n=5, 100, k=1; while(!issquare(n^2+(n+k)^2), k++); s=concat(s, k)); s \\ _Colin Barker_, Mar 31 2014

%o (Python)

%o from sympy.ntheory.primetest import is_square

%o def a(n):

%o     k = 1

%o     while not is_square(n**2 + (n+k)**2): k += 1

%o     return k

%o print([a(n) for n in range(5, 70)]) # _Michael S. Branicky_, Jul 02 2021

%Y Cf. A000290, A055527 (least k>0 such that n^2 + k^2 is a square).

%K nonn

%O 5,1

%A _Alex Ratushnyak_, Mar 30 2014