

A233525


Start with a(1) = 1, a(2) = 1, then a(n)*3^k = a(n+1) + a(n+2), with 3^k the smallest power of 3 (k>0) such that all terms a(n) are positive integers.


2



1, 1, 2, 1, 5, 4, 11, 1, 32, 49, 47, 100, 41, 259, 110, 667, 323, 1678, 1229, 3805, 7256, 4159, 17609, 19822, 33005, 26461, 72554, 6829, 210833, 342316, 290183, 736765, 133784, 2076511, 1535657
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OFFSET

1,3


COMMENTS

Define 3free Fibonacci numbers as sequences where b(n) = (b(n1) + b(n2))/3^i such that 3^i is the greatest power of 2 that divides b(n1) + b(n2). Read backwards from the nth term, this sequence produces a subsequence of 3free Fibonacci numbers where we must divide by a power of 3 every every time we add.
For other examples of nfree Fibonacci numbers, see A232666, A214684, A224382.


LINKS

Brandon Avila, Table of n, a(n) for n = 1..1000
B. Avila and T. 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=1):
....yield a
....yield b
....for i in range(2, n):
........a *= 3
........while a <= b:
............a *= 3
........a, b = b, a  b
........yield b


CROSSREFS

Cf. A233526.
Sequence in context: A056605 A091802 A144240 * A209143 A243274 A119914
Adjacent sequences: A233522 A233523 A233524 * A233526 A233527 A233528


KEYWORD

nonn


AUTHOR

Brandon Avila, Tanya Khovanova, Dec 11 2013


STATUS

approved



