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a(n) = abs((n-th prime of the form 6*k+1) minus (n-th prime of the form 6*m-1))/2.
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%I #8 Feb 18 2019 02:32:01

%S 1,1,1,4,4,1,7,7,7,4,7,7,4,10,13,10,10,7,7,10,10,10,13,1,4,16,13,13,

%T 22,22,25,22,19,25,13,13,19,13,16,16,10,13,10,19,19,28,31,28,34,34,40,

%U 25,25,25,22,25,31,28,25,31,37,37,31,34,28,25,22,25,25,16,22,19,25,22,25

%N a(n) = abs((n-th prime of the form 6*k+1) minus (n-th prime of the form 6*m-1))/2.

%F a(n) = abs(A003627(n+1) - A007645(n+1))/2 = abs(A002476(n) - A007528(n))/2.

%e a(1) = abs(6*1 + 1 - (6*1 - 1))/2 = 1;

%e a(2) = abs(6*2 + 1 - (6*2 - 1))/2 = 1.

%p A002476 := proc(n) if n = 1 then 7; else for a from procname(n-1)+6 by 6 do if isprime(a) then return a; end if; end do: end if; end proc:

%p A007528 := proc(n) if n = 1 then 5; else for a from procname(n-1)+6 by 6 do if isprime(a) then return a; end if; end do: end if; end proc:

%p A171716 := proc(n) A002476(n)-A007528(n) ; abs(%)/2 ; end proc: seq(A171716(n),n=1..120) ; # _R. J. Mathar_, May 22 2010

%Y Cf. A002476, A003627, A007528, A007645.

%K nonn

%O 1,4

%A _Juri-Stepan Gerasimov_, Dec 17 2009

%E a(26) corrected by _R. J. Mathar_, May 22 2010