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%I #10 Aug 03 2022 12:40:28
%S 2,7,11,17,19,29,61,89,97,127,179,251,263,269,277,307,331,397,433,439,
%T 457,467,479,523,569,601,647,739,773,809,863,883,937,953,971,1063,
%U 1087,1091,1171,1181,1307,1447,1483,1511,1583,1621,1657,1663,1783,1789,1801,1811,1879,1889,1933,1951,1987
%N Primes p such that p = 3*a + 1 with p + a*a*(a+1) prime or p = 3*a + 2 with p + a*(a+1)*(a+1) prime.
%C Primes p that can be divided in three parts differing by at most 1 with p + the product of the parts prime.
%H Robert Israel, <a href="/A356003/b356003.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3) = 11 is a term because 11 = 3+4+4 with 11+3*4*4 = 59 prime.
%p filter:= proc(p) local a,t;
%p if not isprime(p) then return false fi;
%p if p mod 3 = 1 then a:= (p-1)/3; t:= p+a^2*(a+1) else a:= (p-2)/3; t:= p+a*(a+1)^2 fi;
%p isprime(t)
%p end proc:
%p select(filter, [2,seq(i,i=5..2000,2)]);
%t q[p_] := Module[{r = Mod[p, 3], a}, a = (p-r)/3; r > 0 && PrimeQ[p+a*(a+1)*(a+r-1)]]; Select[Prime[Range[300]], q] (* _Amiram Eldar_, Jul 22 2022 *)
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Jul 22 2022
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