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A067150
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Number of integers i=1,2,...,n such that (n,i) has Property F3*, i.e., i and n are consecutive terms of a sequence b(k) satisfying b(1)=1, b(n) = (b(n-1) OR 2*b(n-1)) + b(n-2), where the OR is taken bitwise.
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1
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0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 0, 1, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 1, 0, 2, 3, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 1, 1, 1, 0, 1, 2, 0, 3, 5, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0
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OFFSET
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1,16
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COMMENTS
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Surprisingly, for k > 0, we find that a(2^k) = F(k-1), where {F(n)} is the sequence of Fibonacci numbers (A000045). Also, except for n = 2^3 = 8, these values are exactly those where new records in a(n) are made.
The definition can be restated as follows: a(n) is the number of integers i, 0 < i < n such that i and n are consecutive terms of some sequence b(k) satisfying b(1)=1 and b(k) = 3#b(k-1) + b(k-2), where # denotes OR-numbral multiplication (see A048888 for the definition).
If the OR-numbral multiplier 3 in the definition is replaced by 7, the resulting sequence has as record values the tribonacci numbers in A000073.
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LINKS
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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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