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A262097
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a(n) is the number of arithmetic triples k<m<n (three numbers in arithmetic progression) such that k and m contain no 2's in their ternary representation.
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6
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0, 0, 1, 0, 0, 2, 1, 1, 1, 0, 0, 1, 0, 0, 3, 2, 2, 3, 1, 1, 2, 1, 1, 2, 1, 1, 1, 0, 0, 1, 0, 0, 2, 1, 1, 1, 0, 0, 1, 0, 0, 4, 3, 3, 5, 2, 2, 4, 2, 2, 5, 3, 3, 4, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 2, 1, 1, 1, 0, 0
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OFFSET
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0,6
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COMMENTS
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This is a recursive sequence that gives the number of times n is rejected from A005836, if n is the largest member of an arithmetic triple whose initial two terms are contained in A005836.
This is similar to both A002487, which has a similar recurrence relation and counts hyperbinary representations of n, and A000119, which counts representations of n as a sum of distinct Fibonacci numbers.
a(n) is the number of times n occurs in A262096.
Indices of maxima between a(n)=0 and a(k)=0 (choose the smallest k) appear to converge to (1/12)*(k-n) and (1/4)*(k-n). - Max Barrentine, May 24 2016
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LINKS
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Max Barrentine, Table of n, a(n) for n = 0..19683
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FORMULA
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a(0)=0, a(n) = a(3n) = a(3n+1); if a(n)=0, a(3n+2) = a(n+1) + 1, otherwise a(3n+2) = a(n+1) + a(n). - Max Barrentine, May 24 2016
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CROSSREFS
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Cf. A000119, A002487, A005836, A262096, A262256, A273513, A273514.
Sequence in context: A081602 A077267 A134022 * A085975 A277778 A255319
Adjacent sequences: A262094 A262095 A262096 * A262098 A262099 A262100
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KEYWORD
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nonn,look,easy,base
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AUTHOR
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Max Barrentine, Sep 11 2015
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EXTENSIONS
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Name improved by Max Barrentine, Jun 23 2016
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STATUS
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approved
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