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

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).

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 and formula from David W. Wilson May 15 1997

Status

approved