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A146343 a(n) = smallest number k such that the continued fraction of (1 + sqrt(k))/2 has period n. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
Sequence in context: A281842 A282224 A282201 * A146363 A246797 A087958
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

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Last modified March 29 08:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)