A262097 - OEIS

%I #62 Nov 22 2018 20:20:24

%S 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,

%T 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,

%U 3,2,2,3,1,1,2,1,1,2,1,1,1,0,0

%N 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.

%C 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.

%C 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.

%C a(n) is the number of times n occurs in A262096.

%C 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

%H Max Barrentine, <a href="/A262097/b262097.txt">Table of n, a(n) for n = 0..19683</a>

%F 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

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

%K nonn,look,easy,base

%O 0,6

%A _Max Barrentine_, Sep 11 2015

%E Name improved by _Max Barrentine_, Jun 23 2016