A273874 Least positive integer k such that k^2 + (k+1)^2 + ... + (k+n-2)^2 + (k+n-1)^2 is the sum of two nonzero squares. a(n) = 0 if no solution exists.

5, 1, 2, 0, 2, 0, 0, 0, 0, 2, 5, 1, 12, 0, 3, 0, 3, 0, 0, 0, 0, 0, 53, 1, 1, 1, 2, 0, 4, 0, 0, 0, 5, 2, 0, 0, 2, 0, 3, 0, 5, 0, 0, 5, 0, 0, 73, 1, 3, 1, 2, 0, 2, 0, 5, 0, 0, 2, 97, 1, 4, 0, 0, 0, 2, 5, 0, 0, 30, 0, 0, 0, 1, 1, 4, 0, 0, 0, 0, 0, 0, 2, 26, 0, 6

Offset: 1

Author

Altug Alkan, Jun 02 2016

Keywords

• nonn

Comments

Least positive integer k such that Sum_{i=0..n-1} (k+i)^2 = n*(6*k^2 + 6*k*n - 6*k + 2*n^2 - 3*n + 1)/6 is the sum of two nonzero squares. a(n) = 0 if no k exists for corresponding n.

Examples

			a(1) = 5 because 5^2 = 3^2 + 4^2.
a(3) = 2 because 2^2 + 3^2 + 4^2 = 2^2 + 5^2.
		

Crossrefs

Cf. A000404, A034705.

Extensions

a(7)-a(50) from Giovanni Resta, Jun 02 2016

More terms from Jinyuan Wang, May 02 2021