

A273513


a(n) is the number of arithmetic triples n<p<q (three numbers in arithmetic progression) such that p and q contain no 2's in their ternary representation.


4



0, 0, 1, 0, 0, 1, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 2, 2, 3, 0, 0, 1, 0, 0, 1, 1, 1, 2, 0, 0, 1, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 3, 2, 2, 3, 1, 1, 2, 1, 1, 4, 3, 3, 5, 2, 2, 4, 2, 2, 5, 3, 3, 4, 0, 0, 1, 0, 0, 1
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OFFSET

0,9


COMMENTS

This is a recursive sequence that gives the number of times n is rejected from A005836, if n is the smallest member of an arithmetic triple whose final 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.
For n<k (choose the smallest k), a(n)=0, a(k)=0, a(n)=A262097(k), a(n+1)=A262097(k1), a(n+2)=A262097(k2)... a(k)=A262097(n).
Indices of maxima between a(n) and a(k) appear to converge to (3/4)(kn) and (11/12)(kn).


LINKS

Max Barrentine, Table of n, a(n) for n = 0..19683 (terms 1 through 10000 from Robert Israel)
Robert Israel, Plot of first 10^5 terms


FORMULA

a(0)=0, a(n)=a(3n)=a(3n+1);
if a(n+1)=0, a(3n+2)=1+a(n), otherwise a(3n+2)=a(n)+a(n+1).


MAPLE

f:= proc(n) option remember; local m;
m:= floor(n/3);
if n mod 3 <> 2 then procname(m)
elif procname(m+1)=0 then 1 + procname(m)
else procname(m) + procname(m+1)
fi
end proc:
f(0):= 0:
map(f, [$0..100]); # Robert Israel, Jun 16 2016


CROSSREFS

Cf. A000119, A002487, A005836, A262097, A273514.
Sequence in context: A093955 A330168 A081603 * A330005 A165277 A245194
Adjacent sequences: A273510 A273511 A273512 * A273514 A273515 A273516


KEYWORD

nonn,base,look


AUTHOR

Max Barrentine, May 23 2016


STATUS

approved



