login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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(k-1), a(n+2)=A262097(k-2)... a(k)=A262097(n).

Indices of maxima between a(n) and a(k) appear to converge to (3/4)(k-n) and (11/12)(k-n).

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 11 18:00 EDT 2021. Contains 342888 sequences. (Running on oeis4.)