A160273 Successive differences (divided by 3) of the average of twin prime pairs divided by 2 (A040040).

1, 1, 2, 2, 3, 2, 5, 1, 5, 2, 5, 2, 1, 5, 2, 5, 2, 5, 6, 12, 2, 5, 10, 8, 5, 3, 4, 3, 25, 2, 1, 5, 4, 23, 2, 3, 2, 5, 10, 13, 8, 2, 2, 3, 18, 4, 5, 1, 20, 2, 8, 5, 4, 11, 14, 1, 9, 3, 8, 5, 9, 1, 4, 3

Offset: 1

Author

Stephen Crowley, May 07 2009

Keywords

• nonn

Comments

From Eric Snyder, Jul 02 2021: (Start)

Also the successive differences of A002822.

Instances of a(n) = 1 correspond to prime quadruples. (End)

Links

• Eric Snyder, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

Crossrefs

Cf. A040040, A002822.

Programs

Maple

ZL := []; for p to 1000000 do if `and`(isprime(p), isprime(p+2)) then ZL := [op(ZL), ((p+2)^2-p^2)*(1/8)] end if end do; a := [seq((ZL[i+1]-ZL[i])*(1/3), i = 2 .. nops(ZL)-1)]

Mathematica

Rest[(Differences[(Mean/@Select[Partition[Prime[Range[500]],2,1], #[[2]]- #[[1]]==2&])/2])/3] (* Harvey P. Dale, Jun 10 2014 *)

Extensions

Keyword "hard" deleted by Harvey P. Dale, Jun 10 2014