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A180931 Primes p such that their product for the successive prime plus one added to one is a prime: p(i)*[p(i+1)+1]+1 gives a prime.

%I A180931 #12 May 12 2020 16:23:21
%S A180931 3,5,19,23,29,47,53,59,79,137,167,179,233,239,241,263,283,349,353,359,
%T A180931 383,389,419,421,439,491,563,617,653,701,709,719,739,769,797,811,829,
%U A180931 887,1049,1051,1129,1153,1187,1399,1433,1489,1523,1549,1559,1579,1601
%N A180931 Primes p such that their product for the successive prime plus one added to one is a prime: p(i)*[p(i+1)+1]+1 gives a prime.
%C A180931 There are some twin primes in the sequence: (3,5); (239,241); (419, 421); (1607, 1609).
%C A180931 Apparently the sequence is infinite.
%H A180931 Robert Israel, <a href="/A180931/b180931.txt">Table of n, a(n) for n = 1..10000</a>
%e A180931 a(5)=29 since 29*(31+1)+1=29*32+1=929 is a prime.
%p A180931 R:= NULL; count:= 0:
%p A180931 q:= 2:
%p A180931 while count < 100 do
%p A180931   p:= q; q:= nextprime(q);
%p A180931   if isprime(p*(q+1)+1) then count:= count+1; R:= R, p fi
%p A180931 od:
%p A180931 R; # _Robert Israel_, May 12 2020
%t A180931 Select[Prime[Range[350]],PrimeQ[ # (NextPrime[ # ]+1)+1]&] (* _Harvey P. Dale_, Oct 08 2010 *)
%Y A180931 Cf. A000040.
%K A180931 nonn
%O A180931 1,1
%A A180931 _Carmine Suriano_, Sep 26 2010
%E A180931 Added missing terms (5 terms were omitted after 887). _Harvey P. Dale_, Oct 08 2010