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A233526 Start with a(1) = 1, a(2) = 3, then a(n)*2^k = a(n+1) + a(n+2), with 2^k the smallest power of 2 (k>0) such that all terms a(n) are positive integers. 3
1, 3, 1, 5, 3, 7, 5, 9, 1, 17, 15, 19, 11, 27, 17, 37, 31, 43, 19, 67, 9, 125, 19, 231, 73, 389, 195, 583, 197, 969, 607, 1331, 1097, 1565, 629, 2501 (list; graph; refs; listen; history; text; internal format)
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 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=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

Cf. A233525.

Sequence in context: A060819 A318661 A089654 * A097062 A324894 A200498

Adjacent sequences:  A233523 A233524 A233525 * A233527 A233528 A233529

KEYWORD

nonn

AUTHOR

Brandon Avila, Tanya Khovanova, Dec 11 2013

STATUS

approved

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Last modified April 9 06:59 EDT 2020. Contains 333344 sequences. (Running on oeis4.)