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A233526
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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.
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3
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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