The On-Line Encyclopedia of Integer Sequences (OEIS)

A345430 revision #7

A345430

For 1<=x<=n, 1<=y<=n, with gcd(x,y)=1, write 1 = gcd(x,y) = u*x+v*y with u,v minimal; a(n) = sum of the values of |v|.

1, 2, 5, 8, 17, 20, 38, 50, 71, 83, 128, 146, 209, 236, 278, 326, 434, 473, 608, 668, 758, 833, 1031, 1103, 1292, 1400, 1583, 1709, 2024, 2120, 2480, 2672, 2912, 3104, 3410, 3572, 4085, 4328, 4670, 4910, 5540, 5738, 6431, 6761, 7163, 7526, 8354, 8642, 9416, 9788, 10388

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OFFSET

1,2

COMMENTS

Minimal means minimize u^2+v^2. We follow Maple, Pari, etc, in setting u=0 and v=1 when x=y.

LINKS

Table of n, a(n) for n=1..51.

PROG

(Python)

from sympy.core.numbers import igcdex

def A345430(n): return sum(abs(v) for u, v, w in (igcdex(x, y) for x in range(1, n+1) for y in range(1, n+1)) if w == 1) # Chai Wah Wu, Jun 22 2021

CROSSREFS