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
Keywords
Links
- Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe and Georg Fischer)
Programs
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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 *) -
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
Extensions
a(1) corrected by T. D. Noe, Apr 04 2014
a(1) = 26 removed by Georg Fischer, Jun 23 2019