OFFSET
1,2
COMMENTS
A033192(k) is the number of integers m such that a(m) = k. - Michel Marcus, Aug 03 2017
LINKS
Michel Marcus, Table of n, a(n) for n = 1..1000
J. H. E. Cohn, Recurrent Sequences Including N, Fib. Quart., 29-1, 1991.
T. Denes, Problem 413, Discrete Math. 272 (2003), 302 (but there are several errors in the table given there).
James P. Jones, Péter Kiss, Representation of integers as terms of a linear recurrence with maximal index, Acta Academiae Paedagogicae Agriensis, Sectio Mathematicae, 25. (1998) pp. 21-37.
FORMULA
For n>1, a(n) is the largest integer r>1 such that ceiling(((-1)^r*fibonacci(r-2)*n + 1)/fibonacci(r-1)) <= floor(((-1)^r*fibonacci(r-1)*n - 1)/fibonacci(r)), r++). See Theorem 2.12 in Jones & Kiss. - Michel Marcus, Aug 02 2017
MATHEMATICA
max = 12; s[n_] := (1/2)*((3*s1 - s2)*Fibonacci[n] + (s2 - s1)*LucasL[n]); a[n_] := Reap[Do[If[s[m] == n, Sow[m - 1]], {m, 1, max}, {s1, 1, max}, {s2, 1, max}]][[2, 1]] // Max; Table[a[n], {n, 1, 90}] (* Jean-François Alcover, Jan 15 2013 *)
PROG
(PARI) a(n) = {if (n==1, return (1)); r = 2; while (ceil(((-1)^r*fibonacci(r-2)*n + 1)/fibonacci(r-1)) <= floor(((-1)^r*fibonacci(r-1)*n - 1)/fibonacci(r)), r++); r-1; } \\ Michel Marcus, Aug 02 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Don Reble, Nov 20 2003
STATUS
approved