A276689 Least term in the periodic part of the continued fraction expansion of sqrt(n) or 0 if n is square.

0, 0, 2, 1, 0, 4, 2, 1, 1, 0, 6, 3, 2, 1, 1, 1, 0, 8, 4, 1, 2, 1, 1, 1, 1, 0, 10, 5, 2, 1, 2, 1, 1, 1, 1, 1, 0, 12, 6, 4, 3, 2, 2, 1, 1, 1, 1, 1, 1, 0, 14, 7, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 0, 16, 8, 1, 4, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 18, 9, 6, 1

Offset: 0

Author

Chai Wah Wu, Sep 28 2016

Keywords

• nonn

Comments

If r > 0 is even, then a((rm/2)^2+m) = r for all m >= 1 and a((r^2-2)^2/4 + (r+1)^3) = r.

If r is odd, then a((rm)^2+2m) = r for all m >= 1 and a(r^4 + r^3 + 5(r+1)^2/4) = r.

Links

• Chai Wah Wu, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A031424, A003285, A091453, A096491.

Programs

Python

from sympy import continued_fraction_periodic
def A276689(n):
    x = continued_fraction_periodic(0,1,n)
    return min(x[1]) if len(x) > 1 else 0