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Sum of the next n members of the list of twin primes.
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%I #19 Apr 27 2018 21:08:20

%S 3,12,41,120,307,696,1241,1956,3307,5544,8381,12042,16237,21492,27677,

%T 33906,42733,54180,65057,76740,88771,104112,124229,146490,169933,

%U 196884,230807,263790,297475,339372,385349,441900,496375,557628,617357,672510,743917,807888

%N Sum of the next n members of the list of twin primes.

%C Observation: a(26) is also equal to A000521(1) = 196884. - _Omar E. Pol_, Nov 29 2014

%e a(1) = 3, a(2) = 5+7 = 12, a(3) = 11+13+17 = 41, ...

%e a(26) = 7211+7213+7307+7309+7331+7333+7349+7351+7457+7459+7487+7489+7547+7549+7559+ 7561+7589+7591+7757+7759+7877+7879+7949+7951+8009+8011 = 196884. - _Omar E. Pol_, Nov 29 2014

%t With[{nn=100},Total/@TakeList[Union[Flatten[Select[ Partition[Prime[ Range[ 300nn]],2,1],#[[2]]-#[[1]]==2&]]],Range[nn]]] (* Requires Mathematica version 11 or later *) (* _Harvey P. Dale_, Apr 27 2018 *)

%o (PARI) isA001097(n) = (isprime(n) && (isprime(n+2) || isprime(n-2))) ;

%o lista(nn) = {v = select(x->isA001097(x), vector(nn, i, i)); idep = 1; for (n=1, sqrtint(#v), print1(sum(i=idep, idep+n-1, v[i]), ", "); idep += n;);} \\ _Michel Marcus_, Nov 29 2014

%Y Cf. A001097 (twin primes), A007468 (sum of next n primes), A000521.

%K easy,nonn

%O 1,1

%A Den Roussel (DenRoussel(AT)webtv.net)

%E More terms from _Michel Marcus_, Nov 29 2014