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A135274 a(n) = prime(2*n) - prime(2*n-1) + prime(2*n+1).

%I A135274 #13 Oct 08 2016 02:07:52
%S A135274 6,13,19,25,37,47,49,65,69,77,89,103,107,113,131,141,151,159,173,185,
%T A135274 193,199,213,239,235,247,267,275,279,287,317,317,335,353,355,373,385,
%U A135274 393,409,427,433,441,453,469,469,499,503,513,535,565
%N A135274 a(n) = prime(2*n) - prime(2*n-1) + prime(2*n+1).
%C A135274 Original name was: Difference and sum of staircase primes according to the rule: bottom - top + next top.
%C A135274 We list the primes in staircase fashion as follows.
%C A135274 2
%C A135274 3.5
%C A135274 ..7.11
%C A135274 ....13.17
%C A135274 .......19.23
%C A135274 ..........29.31
%C A135274 .............37.41
%C A135274 .....................
%C A135274 ....................n
%C A135274 ....................n+1.n+2.
%C A135274 The right diagonal, RD(n), is the set of top primes and the left diagonal, LD(x), is the set of bottom primes. Then a(n) = LD(n+1) - RD(n) + RD(n+2).
%H A135274 G. C. Greubel, <a href="/A135274/b135274.txt">Table of n, a(n) for n = 1..1000</a>
%F A135274 a(n) = A181428(2*n-1). - _R. J. Mathar_, Sep 10 2016
%t A135274 Join[{6},#[[3]]-#[[2]]+#[[4]]&/@Partition[Prime[Range[2,110]],4,2]] (* _Harvey P. Dale_, Nov 16 2011 *)
%o A135274 (PARI) g(n) = forstep(x=1,n,2,y=prime(x+1)-prime(x)+prime(x+2);print1(y","))
%o A135274 (PARI) a(n)=prime(2*n)-prime(2*n-1)+prime(2*n+1); \\ _Joerg Arndt_, Oct 08 2016
%K A135274 nonn,easy
%O A135274 1,1
%A A135274 _Cino Hilliard_, Dec 02 2007
%E A135274 New name from _Joerg Arndt_, Oct 08 2016