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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.)