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a(n) = A001097(n) + A001097(n+1).
0

%I #16 Jan 15 2017 08:31:56

%S 8,12,18,24,30,36,48,60,72,84,102,120,132,144,174,204,210,216,246,276,

%T 288,300,330,360,372,384,390,396,426,456,468,480,510,540,552,564,594,

%U 624,660,696,768,840,852,864,894,924,984,1044,1092,1140

%N a(n) = A001097(n) + A001097(n+1).

%F a(n) = 2*A163656(n).

%t Total /@ Partition[#, 2, 1] &@ Select[Prime@ Range@ 105, Total@ Boole@ Map[PrimeQ, # + 2 {-1, 1}] > 0 &] (* _Michael De Vlieger_, Jan 11 2017 *)

%o (PARI) {

%o t=4;

%o forstep(n=6,1000,6,

%o if(isprime(n-1)&&isprime(n+1),

%o k=2*n;print1((k+t)/2", ")

%o ;print1(k", ");t=k

%o )

%o )

%o }

%Y Cf. A001097. Essentially the same as A096281. A163656.

%K nonn

%O 1,1

%A _Dimitris Valianatos_, Jan 11 2017