A004794 - OEIS

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A004794

Least positive integer k such that the fractional part of k*sqrt(5) has its n initial partial quotients all equal to 1.

3, 7, 7, 28, 45, 189, 799, 2091, 2091, 8856, 14329, 60697, 257115, 673135, 673135, 2851444, 4613733, 19544085, 82790071, 216747219, 216747219, 918155952, 1485607537, 6293134513, 26658145587, 69791931223, 69791931223, 295643364940

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..28.

FORMULA

a(n) = (Fib(12[ n/6 ] + S_(n mod 6))+1)/2 where S = (2, 5, 7, 7, 10, 11). - David W. Wilson, May 15 1997

Empirical g.f.: -x*(x^12 -x^10 +3*x^9 +4*x^7 -356*x^6 +144*x^5 +17*x^4 +21*x^3 +4*x +3) / ((x -1)*(x^2 -3*x +1)*(x^2 +3*x +1)*(x^4 -3*x^3 +8*x^2 -3*x +1)*(x^4 +3*x^3 +8*x^2 +3*x +1)). - Colin Barker, Jul 14 2013

CROSSREFS

Sequence in context: A322934 A077629 A184467 * A336719 A272981 A086839

Adjacent sequences: A004791 A004792 A004793 * A004795 A004796 A004797

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

More terms from David W. Wilson, May 15 1997

STATUS

approved