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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. 2
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..80.

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 A129756

Adjacent sequences:  A190265 A190266 A190267 * A190269 A190270 A190271

KEYWORD

nonn

AUTHOR

Juri-Stepan Gerasimov, May 06 2011

STATUS

approved

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Last modified March 30 11:16 EDT 2020. Contains 333125 sequences. (Running on oeis4.)