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%I #8 Jul 16 2022 11:54:20
%S 3,5,13,17,19,29,41,47,61,67,73,97,103,107,157,191,229,277,281,283,
%T 293,307,379,401,409,491,547,557,569,607,619,659,691,701,751,773,787,
%U 823,827,853,883,887,911,971,983,997,1031,1039,1049,1109,1129,1153,1171
%N Primes such that their product with the successive prime plus the next successive prime plus 1 is a prime.
%C prime(i)*prime(i+1) + prime(i+2) + 1 is prime.
%C In the sequence there are some twins: e.g. (281, 283) and (1949, 1951).
%C There are also successive primes such as (13,17,19); (277,281,283,293,307); (883,887).
%e a(5)=19 since 19*23+29+1=467 is a prime.
%t #[[1]]&/@Select[Partition[Prime[Range[200]],3,1],PrimeQ[ #[[1]] #[[2]]+#[[3]]+1]&] (* _Harvey P. Dale_, Nov 07 2010 *)
%Y Cf. A000040.
%K nonn
%O 1,1
%A _Carmine Suriano_, Sep 27 2010
%E Missing values starting at 1031 inserted by _R. J. Mathar_, Oct 18 2010