A146343 a(n) = smallest number k such that the continued fraction of (1 + sqrt(k))/2 has period n.

5, 2, 17, 6, 41, 18, 89, 31, 73, 43, 265, 94, 421, 118, 193, 172, 521, 106, 241, 151, 337, 489, 433, 268, 929, 211, 409, 334, 673, 379, 937, 463, 601, 331, 769, 721, 2297, 619, 1033, 718, 1777, 394, 1753, 604, 1993, 634, 1249, 526, 3649, 694

Offset: 1

Author

Artur Jasinski, Oct 30 2008

Keywords

• nonn

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000290, A078370, A146326-A146345, A146348-A146360.

Programs

Maple

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

Mathematica

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

Extensions

a(6) changed to 18, a(25) to 929, a(28) to 334 by R. J. Mathar, Nov 08 2008

Extended by T. D. Noe, Mar 22 2011