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

Author

Clark Kimberling

Keywords

• nonn

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

Extensions

More terms from David W. Wilson, May 15 1997