A229140 Smallest k such that k^2 + l^2 = n-th number expressible as sum of two squares (A001481).

0, 0, 1, 0, 1, 2, 0, 1, 2, 0, 1, 3, 2, 0, 1, 2, 4, 3, 0, 1, 2, 4, 3, 0, 1, 4, 2, 3, 5, 0, 1, 2, 6, 3, 5, 4, 0, 1, 2, 5, 3, 4, 7, 0, 1, 2, 5, 3, 7, 4, 6, 0, 1, 2, 8, 3, 6, 4, 0, 1, 5, 2, 7, 3, 6, 4, 9, 8, 0, 1, 2, 3, 6, 9, 4, 7, 5, 0, 1, 2, 9, 3, 8, 4, 7, 5, 0

Offset: 1

Author

Ralf Stephan, Sep 15 2013

Keywords

• nonn

Comments

Conjecture: the values between two zeros are always distinct from each other.

Examples

			The 6th number expressible as sum of two squares A001481(6) = 8 = 2^2 + 2^2, so a(6)=2.
		

Crossrefs

Cf. A001481, A385236 (largest k), A385237, A283303, A283304.

Programs

PARI

for(n=0, 300, s=sqrtint(n); forstep(i=s, 0, -1, if(issquare(n-i*i), print1(sqrtint(n-i*i), ", "); break))); \\ shift corrected by Michel Marcus, Jul 08 2025

Formula

a(n) = 0 if A001481(n) is square.

a(n) = sqrt(A001481(n)-A385236(n)^2). - Zhuorui He, Jul 08 2025