

A328216


WeakFibonacciNiven numbers: numbers divisible by the number of terms in at least one representation as a sum of distinct Fibonacci numbers.


0



1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 13, 14, 15, 16, 18, 21, 22, 24, 26, 27, 28, 30, 32, 34, 35, 36, 39, 40, 42, 44, 45, 48, 50, 52, 55, 56, 57, 58, 60, 63, 64, 65, 66, 68, 69, 70, 72, 75, 76, 78, 80, 81, 84, 85, 89, 90, 92, 93, 94, 95, 96, 99, 100, 102, 104, 105, 108
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OFFSET

1,2


COMMENTS

The Fibonacci numbers F(1) = F(2) = 1 can be used at most once in the representation.
Grundman proved that there are infinitely many runs of 6 consecutive weakFibonacciNiven numbers by showing that if m = F(240k) + F(14) + F(9) for k >= 1, then m, m+1, ... m+5 are 6 consecutive weakFibonacciNiven numbers.


LINKS

Table of n, a(n) for n=1..67.
Helen G. Grundman, Consecutive ZeckendorfNiven and lazyFibonacciNiven numbers, Fibonacci Quarterly, Vol. 45, No. 3 (2007), pp. 272276.


EXAMPLE

6 is in the sequence since it can be represented as the sum of 2 Fibonacci numbers, 1 + 5, and 2 is a divisor of 6.


MATHEMATICA

m = 10; v = Array[Fibonacci, m, 2]; vm = v[[1]]; seq = {}; Do[s = Subsets[v, 2^m, {k}]; If[(sum = Total @@ s) <= vm && Divisible[sum, Length @@ s], AppendTo[seq, sum]] , {k, 2, 2^m}]; Union @ seq


CROSSREFS

Supersequence of A328208 and A328212.
Cf. A000045, A005349.
Sequence in context: A192188 A039268 A039162 * A071959 A176845 A196127
Adjacent sequences: A328213 A328214 A328215 * A328217 A328218 A328219


KEYWORD

nonn


AUTHOR

Amiram Eldar, Oct 07 2019


STATUS

approved



