OFFSET
1,2
COMMENTS
Ohtsuka's (2023) problem does not include 1, and includes the even powers of 8 twice (once as powers of Fibonacci(6) = 8 and once as powers of Fibonacci(3) = 2). The sum of reciprocals in this case is (61 - 15*sqrt(5))/18.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..1000
Hideyuki Ohtsuka, Problem B-1321, Elementary Problems and Solutions, The Fibonacci Quarterly, Vol. 61, No. 1 (2023), p. 84.
FORMULA
Sum_{n>=1} 1/a(n) = 551/126 - 5*sqrt(5)/6.
MATHEMATICA
seq[max_] := Module[{s = {1}, k = 3, f, d}, While[(f = Fibonacci[k]) <= max, If[k != 6, d = 2 - Mod[k, 2]; s = Join[s, f^Range[d, Floor[Log[f, max]], d]]]; k++]; Sort[s]]; seq[10^5]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Feb 20 2023
STATUS
approved