%I #10 Jan 03 2020 07:48:07
%S 2,3,5,41,89,131,743,761,3449,6173,9059,10781,11549,13553,14939,15569,
%T 16301,27809,33479,54773,55439,57149,70901,71849,76091,97523,103391,
%U 103643,104369,110543,114269,115499,140111,141539,153509,161033,162251
%N Prime numbers p such that 2*p+1, p*(p + 1) - 1 and p*(p + 1) + 1 are also primes.
%H Amiram Eldar, <a href="/A136015/b136015.txt">Table of n, a(n) for n = 1..10000</a>
%e 3 is a term since it is a prime, 2 * 3 + 1 = 7 is a prime, 3 * (3 + 1) = 12, and (11, 13) are twin primes.
%p a:=proc(n) if isprime(n)=true and isprime(2*n+1)=true and isprime(n*(n+1)-1)= true and isprime(n*(n+1)+1)=true then n else end if end proc: seq(a(n),n=1.. 150000); # _Emeric Deutsch_, Apr 01 2008
%t a = ""; For[i = 1, i < 10^5, j = i + 1; s = i + j; m = i*j; p1 = m - 1; p2 = m + 1;If[PrimeQ[i] && PrimeQ[s] && PrimeQ[p1] && PrimeQ[p2],a = a <> ToString[i] <> ","]; i++ ]; Print[a <> ".."]
%t Select[Prime[Range[100000]], PrimeQ[2# + 1] && PrimeQ[ #*(# + 1) - 1] && PrimeQ[ #*(# + 1) + 1] &] (* _Stefan Steinerberger_, Mar 24 2008 *)
%K nonn
%O 1,1
%A _Vladimir Joseph Stephan Orlovsky_, Mar 21 2008
%E Edited with more terms by _Stefan Steinerberger_ and _Emeric Deutsch_, Mar 24 2008