A273514 a(n) is the number of arithmetic progressions m < n < p (three numbers in arithmetic progression) such that m and p contain no 2's in their ternary representation.

0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 8, 8, 8, 8, 2, 2, 8, 2, 2, 2, 2, 2, 2, 2, 2, 8, 2, 2, 2, 2, 2, 2, 0, 0, 2, 0, 0, 2

Offset

0,3

Comments

This is a recursive sequence that gives the number of times n is rejected from A005836, if n is the middle member of an arithmetic triple whose first and last terms are contained in A005836.

Also, a(n) is the number of unordered pairs of members of A005836 whose average (arithmetic mean) is n.

It appears that when A273513(n) and A262097(n) are coprime, a(n) = 2.

Local maxima occur at a(A125857(n)).

Links

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

Formula

a(0) = 0, a(n) = a(3n) = a(3n+1); if a(n) = 0, a(9n + 2) = 2, otherwise a(9n + 2) = 4a(n); a(9n + 5) = a(9n + 6) = a(9n + 7) = a(9n + 8) = a(3n + 2).

Example

a(2) = 2 because there are two arithmetic triples a < 2 < b such that a and b are members of A005836: 0, 2, 4 and 1, 2, 3.

Prog

(PARI) precCantor(n)=my(v=digits(n, 3)); for(i=1, #v, if(v[i]==2, for(j=i, #v, v[j]=1); break)); fromdigits(v, 2)
a(n)=if(n==0, return(0)); sum(i=0, precCantor(n-1), my(m=fromdigits(digits(i, 2), 3)); vecmax(digits(2*n-m, 3))<2) \\ Charles R Greathouse IV, Jun 17 2016

Crossrefs

Cf. A005836, A125857, A262097, A273513.

Sequence in context: A318178 A363485 A283307 * A048866 A262904 A144377

Adjacent sequences: A273511 A273512 A273513 * A273515 A273516 A273517

Keyword

nonn,base

Author

Max Barrentine, May 23 2016

Status

approved