# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a031416 Showing 1-1 of 1 %I A031416 #20 Aug 18 2021 00:33:16 %S A031416 89,149,193,218,250,277,337,493,521,569,653,709,914,1009,1018,1037, %T A031416 1385,1465,1553,1597,1618,1754,1781,1898,1921,1973,1994,2069,2129, %U A031416 2146,2293,2378,2389,2441,2474,2561,2725,2741,2777,2897,2957,2986,3170,3229,3265 %N A031416 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 3. %H A031416 T. D. Noe, Table of n, a(n) for n = 1..1000 %t A031416 n = 1; t = {}; While[Length[t] < 60, n++; If[! IntegerQ[Sqrt[n]], c = ContinuedFraction[Sqrt[n]]; len = Length[c[[2]]]; If[OddQ[len] && c[[2, (len + 1)/2]] == 3, AppendTo[t, n]]]]; t (* _T. D. Noe_, Apr 03 2014 *) %t A031416 cfo3Q[n_]:=Module[{s=Sqrt[n],cf,len},cf=If[IntegerQ[s],{0,0}, ContinuedFraction[ s ][[2]]];len=Length[cf];OddQ[len]&&cf[[ (len+1)/2]] == cf[[(len-1)/2]]==3]; Select[Range[3300],cfo3Q] (* _Harvey P. Dale_, Sep 25 2019 *) %Y A031416 Cf. A031404-A031423. %Y A031416 Subsequence of A003814. %K A031416 nonn %O A031416 1,1 %A A031416 _David W. Wilson_ %E A031416 Initial 10 removed by _T. D. Noe_, Apr 03 2014 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE