A262256 -id:A262256 - cp's OEIS frontend

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

Max Barrentine, Sep 11 2015

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

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

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

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

Name improved by Max Barrentine, Jun 23 2016

A262096 Triangle read by rows: numbers c from the set of arithmetic triples a < b < c (three numbers in arithmetic progression) where a and b are terms of A005836.

Original entry on oeis.org

2, 6, 5, 8, 7, 5, 18, 17, 15, 14, 20, 19, 17, 16, 11, 24, 23, 21, 20, 15, 14, 26, 25, 23, 22, 17, 16, 14, 54, 53, 51, 50, 45, 44, 42, 41, 56, 55, 53, 52, 47, 46, 44, 43, 29, 60, 59, 57, 56, 51, 50, 48, 47, 33, 32, 62, 61, 59, 58, 53, 52, 50, 49, 35, 34, 32

Offset: 1

Max Barrentine, Sep 10 2015

The first term in each row of the triangle is a term of A005823; these are also the local maxima. From this term until the next row, the first differences are A236313.

			Each term is generated from arithmetic sequences started from pairs of terms from A005836. The order is according to the arithmetic triples 0, 1, a(1)=2; 0, 3, a(2)=6; 1, 3, a(3)=5; 0, 4, a(4)=8; 1, 4, a(5)=7; 3, 4, a(6)=5; ...
As a triangle, sequence starts:
   2;
   6,  5;
   8,  7,  5;
  18, 17, 15, 14;
  20, 19, 17, 16, 11;
  24, 23, 21, 20, 15, 14;
  26, 25, 23, 22, 17, 16, 14;
  54, 53, 51, 50, 45, 44, 42, 41;
  ...

Max Barrentine, Table of n, a(n) for n = 1..2016

Cf. A005823, A005836, A074940, A236313, A262097, A262256.

isok(n) = (n==0) || (vecmax(digits(n, 3)) != 2);
lista(nn) = {oks = select(x->isok(x), vector(nn, n, n-1)); for (n=2, #oks, for (k=1, n-1, print1(2*oks[n]-oks[k], ", ");););} \\ Michel Marcus, Sep 12 2015

Name corrected by Max Barrentine, May 24 2016

cp's OEIS Frontend

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

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