This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A060215 #39 Jul 20 2024 20:43:12
%S A060215 2,3,7,7,13,58,58,135,461,819,2081,13624,13834,35955,95773,244647,
%T A060215 639389,1798800,4374866,11448871,30002701,78439683,205337953,
%U A060215 541653136,1407271538
%N A060215 Least a(n) such that the period of continued fraction for sqrt(a(n)) has at least n successive 1's.
%C A060215 a(25) <= 3684200835. - _Chai Wah Wu_, Jul 20 2024
%e A060215 n a(n) C.f. period
%e A060215 0 2 1 2
%e A060215 1 3 2 1,2
%e A060215 2 7 4 1,1,1,4
%e A060215 3 7 4 1,1,1,4
%e A060215 4 13 5 1,1,1,1,6
%e A060215 5 58 7 1,1,1,1,1,1,14
%e A060215 6 58 7 1,1,1,1,1,1,14
%e A060215 7 135 8 1,1,1,1,1,1,1,22
%e A060215 8 461 15 2,8,10,1,1,1,1,1,1,1,1,10,8,2,42
%e A060215 9 819 10 1,1,1,1,1,1,1,1,1,56
%e A060215 10 2081 11 1,1,1,1,1,1,1,1,1,1,90
%e A060215 11 13624 62 1,2,1,...,4,5,1,1,1,1,1,1,1,1,1,1,1,5,4,...,1,2,1,232
%e A060215 12 13834 13 1,1,1,1,1,1,1,1,1,1,1,1,234
%e A060215 13 35955 14 1,1,1,1,1,1,1,1,1,1,1,1,1,378
%e A060215 14 95773 25 2,8,2,8,154,1,1,1,1,1,1,1,1,1,1,1,1,1,1,154,8,2,8,2,618
%e A060215 15 244647 16 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,988
%e A060215 16 639389 17 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1598
%e A060215 17 1798800 160 5,5,1,19,...,2,60,(17 1's),60,2,...,19,1,5,5,2682
%e A060215 18 4374866 19 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,4182
%e A060215 19 11448871 20 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,6766
%e A060215 20 30002701 35 2,8,2,8,2,8,2738,(20 1's),738,8,2,8,2,8,2,10954
%e A060215 21 78439683 22 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,17712
%e A060215 22 205337953 23 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,28658
%e A060215 23 541653136 1442 2,3,1,...,4,581,(23 1's),581,4,...,1,3,2,46546
%e A060215 24 1407271538 25 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,75026
%t A060215 Table[Block[{k = 2}, While[NoneTrue[Map[Length, Select[If[IntegerQ@ #, {{#}}, Split@ Last@ ContinuedFraction@ #] &@ Sqrt@ k, First@ # == 1 &]], # >= n &], k++]; k], {n, 14}] (* _Michael De Vlieger_, Oct 26 2017 *)
%o A060215 (PARI) print1("2, 3, 7, ");n=3;for(k=1,10^6,v=contfrac(sqrt(k));s=0; for(l=1,length(v)-n,if(v[l]==1,s=s+1,s=0);if(s==n,print1(k", ");n=n+1;k=k-1;break)))
%Y A060215 Cf. A071296.
%K A060215 nonn,more
%O A060215 0,1
%A A060215 _Jeff Burch_, Mar 21 2001
%E A060215 More terms from _Ralf Stephan_, Mar 26 2003
%E A060215 Definition clarified by _T. D. Noe_, Apr 07 2014
%E A060215 a(11), a(14) corrected and a(17)-a(23) added by _Lars Blomberg_, Oct 24 2015
%E A060215 a(0), a(24) from _Chai Wah Wu_, Sep 23 2019