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

Author

Juri-Stepan Gerasimov, May 06 2011

Keywords

• nonn

Comments

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

Examples

			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
		

Links

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

Crossrefs

Cf. A001359, A006512, A014574, A178670.

Programs

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