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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. 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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 28 00:54 EDT 2021. Contains 346316 sequences. (Running on oeis4.)