A262097 a(n) is the number of arithmetic triples k

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

Author

Max Barrentine, Sep 11 2015

Keywords

• nonn
• look
• easy
• base

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

Crossrefs

Cf. A000119, A002487, A005836, A262096, A262256, A273513, A273514.

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

Extensions

Name improved by Max Barrentine, Jun 23 2016