OFFSET
1,2
COMMENTS
Define 2-free Fibonacci numbers as sequences where b(n) = (b(n-1) + b(n-2))/2^i such that 2^i is the greatest power of 2 that divides b(n-1) + b(n-2). Read backwards from the n-th term, this sequence produces a subsequence of 2-free Fibonacci numbers where we must divide by a power of 2 every time we add.
LINKS
Brandon Avila, Table of n, a(n) for n = 1..1000
Brandon Avila and Tanya Khovanova, Free Fibonacci Sequences, arXiv preprint arXiv:1403.4614 [math.NT], 2014 and J. Int. Seq. 17 (2014) # 14.8.5.
PROG
(Python)
def minDivisionRich(n, a=1, b=3):
....yield a
....yield b
....for i in range(2, n):
........a *= 2
........while a <= b:
............a *= 2
........a, b = b, a - b
........yield b
CROSSREFS
KEYWORD
nonn
AUTHOR
Brandon Avila and Tanya Khovanova, Dec 11 2013
STATUS
approved