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%I #15 Nov 20 2023 00:05:26
%S 5,2,17,6,41,18,89,31,73,43,265,94,421,118,193,172,521,106,241,151,
%T 337,489,433,268,929,211,409,334,673,379,937,463,601,331,769,721,2297,
%U 619,1033,718,1777,394,1753,604,1993,634,1249,526,3649,694
%N a(n) = smallest number k such that the continued fraction of (1 + sqrt(k))/2 has period n.
%H T. D. Noe, <a href="/A146343/b146343.txt">Table of n, a(n) for n = 1..1000</a>
%p A := proc(n) local c; try c := numtheory[cfrac](1/2+sqrt(n)/2,'periodic','quotients') ; RETURN(nops(c[2]) ); catch: RETURN(-1) end try ; end: A146343 := proc(n) for k from 1 do if A(k) = n then RETURN(k); fi; od: end: for n from 1 to 30 do printf("%d,",A146343(n)) ; od: # _R. J. Mathar_, Nov 08 2008
%t nn = 50; t = Table[0, {nn}]; cnt = 0; k = 1; While[cnt < nn, k++; cf = ContinuedFraction[(1 + Sqrt[k])/2]; If[Head[cf[[-1]]] === List, len = Length[cf[[-1]]]; If[len <= nn && t[[len]] == 0, t[[len]] = k; cnt++]]]; t
%Y Cf. A000290, A078370, A146326-A146345, A146348-A146360.
%K nonn
%O 1,1
%A _Artur Jasinski_, Oct 30 2008
%E a(6) changed to 18, a(25) to 929, a(28) to 334 by _R. J. Mathar_, Nov 08 2008
%E Extended by _T. D. Noe_, Mar 22 2011
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