A013944 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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