A146343 - OEIS

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

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OFFSET

1,1

LINKS

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

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

CROSSREFS

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

Sequence in context: A281842 A282224 A282201 * A146363 A246797 A087958

Adjacent sequences: A146340 A146341 A146342 * A146344 A146345 A146346

KEYWORD

nonn

AUTHOR

Artur Jasinski, Oct 30 2008

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

STATUS

approved