A013944 Sum of terms in period of continued fraction for square root of the n-th nonsquare.

2, 3, 4, 6, 7, 5, 6, 9, 8, 10, 10, 7, 8, 12, 17, 10, 14, 18, 13, 9, 10, 15, 18, 16, 12, 25, 13, 14, 16, 11, 12, 18, 16, 15, 16, 14, 29, 20, 20, 34, 19, 13, 14, 21, 26, 22, 26, 20, 16, 22, 20, 27, 18, 36, 22, 15, 16, 24, 41, 20, 34, 24, 33, 18, 30, 20, 19, 40

Offset

1,1

Links

Table of n, a(n) for n=1..68.

Mathematica

Table[If[IntegerQ[Sqrt[n]], {}, Total[ContinuedFraction[Sqrt[n]][[2]]]], {n, 100}]//Flatten (* Harvey P. Dale, Apr 26 2016 *)

Prog

(Python)
from math import isqrt
from sympy.ntheory.continued_fraction import continued_fraction_periodic
def A013944(n): return sum(continued_fraction_periodic(0, 1, n+(k:=isqrt(n))+int(n>=k*(k+1)+1))[-1]) # Chai Wah Wu, Jul 20 2024

Crossrefs

Sequence in context: A071373 A344412 A143102 * A123497 A123501 A073210

Adjacent sequences: A013941 A013942 A013943 * A013945 A013946 A013947

Keyword

nonn

Author

Clark Kimberling

Extensions

Definition corrected by Clark Kimberling, Apr 21 2010

Corrected by Harvey P. Dale, Apr 26 2016

Status

approved