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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Define 3-free Fibonacci numbers as sequences where b(n) = (b(n-1) + b(n-2))/3^i such that 3^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 3-free Fibonacci numbers where we must divide by a power of 3 every every time we add.

For other examples of n-free 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

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Last modified March 30 09:49 EDT 2020. Contains 333125 sequences. (Running on oeis4.)