A190268 Number of ways to express the n-th average of a twin prime pair as the arithmetic mean of a lower and an upper twin prime.

1, 1, 3, 3, 3, 3, 5, 5, 5, 3, 3, 13, 3, 5, 1, 3, 7, 9, 5, 7, 1, 15, 5, 7, 3, 9, 9, 3, 7, 13, 11, 3, 3, 7, 9, 13, 3, 23, 13, 15, 7, 13, 5, 21, 11, 9, 9, 13, 9, 5, 3, 15, 3, 9, 11, 9, 9, 9, 17, 15, 5, 7, 9, 7, 7, 21, 19, 7, 11, 43, 35, 11, 25, 11, 5, 7, 7, 37, 27, 9

Offset

1,3

Comments

Number of ways to write 2*A014574(n) as a sum of an element of A001359 plus an element of A006512.

Links

Robert Israel, Table of n, a(n) for n = 1..5000

Example

a(7)=5 because the 7th average is A014574(7)=60 which equals the five averages of the pairs (11,109), (17,103), (59,61), (101,19) and (107,13). - R. J. Mathar, Jun 03 2011

Maple

isA001359 := proc(n) isprime(n) and isprime(n+2) ; end proc:
A001359 := proc(n) option remember; local a; if n = 1 then 3 ; else for a from procname(n-1)+2 by 2 do if isA001359(a) then return a; end if; end do: end if; end proc:
isA006512 := proc(n) isprime(n) and isprime(n-2) ; end proc:
A190268 := proc(n) local a, avn, lowtp, uptp, k ; a := 0 ; avn := A014574(n) ; for k from 1 do lowtp := A001359(k) ; uptp := 2*avn-lowtp ; if uptp <= 0 then break; end if; if isA006512(uptp) then a := a+1 ; end if; end do: a ; end proc:
seq(A190268(n), n=1..80) ; # R. J. Mathar, May 26 2011

Crossrefs

Cf. A001359, A006512, A014574, A178670.

Sequence in context: A332323 A162220 A118911 * A111756 A130821 A352226

Adjacent sequences: A190265 A190266 A190267 * A190269 A190270 A190271

Keyword

nonn

Author

Juri-Stepan Gerasimov, May 06 2011

Status

approved