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%I #24 Nov 02 2023 02:22:36
%S 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,
%T 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,
%U 5,7,9,7,7,21,19,7,11,43,35,11,25,11,5,7,7,37,27,9
%N 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.
%C Number of ways to write 2*A014574(n) as a sum of an element of A001359 plus an element of A006512.
%H Robert Israel, <a href="/A190268/b190268.txt">Table of n, a(n) for n = 1..5000</a>
%e 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
%p isA001359 := proc(n) isprime(n) and isprime(n+2) ; end proc:
%p 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:
%p isA006512 := proc(n) isprime(n) and isprime(n-2) ; end proc:
%p 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:
%p seq(A190268(n),n=1..80) ; # _R. J. Mathar_, May 26 2011
%Y Cf. A001359, A006512, A014574, A178670.
%K nonn
%O 1,3
%A _Juri-Stepan Gerasimov_, May 06 2011
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