A262097 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.

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

Offset

0,6

Comments

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

Links

Max Barrentine, Table of n, a(n) for n = 0..19683

Formula

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

Crossrefs

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

Keyword

nonn,look,easy,base

Author

Max Barrentine, Sep 11 2015

Extensions

Name improved by Max Barrentine, Jun 23 2016

Status

approved