

A031749


Numbers k such that the least term in the periodic part of the continued fraction for sqrt(k) is 71.


7



5043, 20168, 45375, 80664, 126035, 181488, 247023, 322640, 408339, 504120, 609983, 725928, 851955, 988064, 1134255, 1290528, 1456883, 1633320, 1819839, 2016440, 2223123, 2439888, 2666735, 2903664, 3150675, 3407768, 3674943, 3952200, 4239539
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OFFSET

1,1


COMMENTS

The continued fraction expansion of sqrt((j*m)^2+t*m) for m >= 1 where t divides 2*j has the form [j*m, 2*j/t, 2*j*m, 2*j/t, 2*j*m, ...]. Thus numbers of the form (71*m)^2 + 2*m for m >= 1 are in the sequence. Are there any others?  Chai Wah Wu, Jun 18 2016
The term 25776072 is not of the form (71*m)^2 + 2*m.  Chai Wah Wu, Jun 19 2016


LINKS



MATHEMATICA

lt71Q[n_]:=Module[{s=Sqrt[n]}, If[IntegerQ[s], 0, Min[ContinuedFraction[s] [[2]]]] == 71]; Select[Range[43*10^5], lt71Q] (* Harvey P. Dale, Apr 11 2017 *)


PROG

(Python)
from sympy import continued_fraction_periodic
A031749_list = [n for n, d in ((n, continued_fraction_periodic(0, 1, n)[1]) for n in range(1, 10**5)) if isinstance(d, list) and min(d) == 71] # Chai Wah Wu, Jun 09 2017


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



