A239975 Least k>0 such that n^2 + (n+k)^2 is a square, or -1 if no such k exists.

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, 10, 449, 28, 11, 254, 49, 12, 647, 322, 13, 2, 799, 14, 881, 73, 15, 482, 1057, 7, 119, 70, 17, 113, 1351, 18, 77, 34, 19, 782, 1681, 3, 1799, 898, 21, 56, 7, 22, 2177, 217, 23

Offset: 5

Author

Alex Ratushnyak, Mar 30 2014

Keywords

• nonn

Comments

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

Examples

			a(6) = 2 because 6^2 + (6+2)^2 = 100 is a square.
a(20) = 1 because 20^2 + 21^2 = 841 = 29^2.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 5..10004

Crossrefs

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

Programs

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

Python

from sympy.ntheory.primetest import is_square
def a(n):
    k = 1
    while not is_square(n**2 + (n+k)**2): k += 1
    return k
print([a(n) for n in range(5, 70)]) # Michael S. Branicky, Jul 02 2021