A031423 Numbers k such that the continued fraction for sqrt(k) has odd period and if the last term of the periodic part is deleted then there are a pair of central terms both equal to 10.

701, 1418, 1493, 2197, 2290, 3257, 4793, 6154, 6466, 8389, 8753, 9577, 9965, 10765, 11257, 11677, 12541, 14218, 14929, 15413, 15658, 16001, 16501, 17009, 17786, 18049, 18314, 18581, 19121, 21577, 22157, 22745, 24557, 24677, 25805, 26561, 27530, 28517

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe and Georg Fischer)

Mathematica

n = 1; t = {}; While[Length[t] < 50, n++; If[! IntegerQ[Sqrt[n]], c = ContinuedFraction[Sqrt[n]]; len = Length[c[[2]]]; If[OddQ[len] && c[[2, (len + 1)/2]] == 10 && c[[2, (len + 1)/2 - 1]] == 10, AppendTo[t, n]]]]; t (* T. D. Noe, Apr 04 2014; corrected by Georg Fischer, Jun 23 2019 *)

Prog

(Python)
from sympy.ntheory.continued_fraction import continued_fraction_periodic
A031423_list = []
for n in range(1, 10**4):
    cf = continued_fraction_periodic(0, 1, n)
    if len(cf) > 1 and len(cf[1]) > 1 and len(cf[1]) % 2 and cf[1][len(cf[1])//2] == 10:
        A031423_list.append(n) # Chai Wah Wu, Sep 16 2021

Crossrefs

Cf. A031404-A031422.

Subsequence of A003814.

Sequence in context: A093235 A223351 A180469 * A140433 A316969 A303689

Adjacent sequences: A031420 A031421 A031422 * A031424 A031425 A031426

Keyword

nonn

Author

David W. Wilson

Extensions

a(1) corrected by T. D. Noe, Apr 04 2014

a(1) = 26 removed by Georg Fischer, Jun 23 2019

Status

approved