cp's OEIS Frontend

A216880 Numbers of the form 3p - 2 where p and 6p + 1 are prime.

%I A216880 #31 Mar 04 2023 16:24:32
%S A216880 4,7,13,19,31,37,49,67,109,139,181,217,247,301,307,319,391,409,451,
%T A216880 517,541,697,721,769,787,811,829,847,877,931,937,991,1039,1099,1117,
%U A216880 1189,1327,1381,1399,1507,1669,1729,1777,1801,1819,1921,1957,1981,2047,2179,2251,2281
%N A216880 Numbers of the form 3p - 2 where p and 6p + 1 are prime.
%C A216880 This formula produces many primes and semiprimes.
%C A216880 Taken just the terms from the sequence above:
%C A216880 n is prime for the following values of p: 3, 5, 7, 11, 13, 23, 37, 47, 61, 103, 137, 181, 257, 263, 271, 277, 293, 313, 331, 347, 373, 443, 461, 467, 557, 593, 601, 727, 751, 761.
%C A216880 n is a semiprime of the form (6*m + 1 )*(6*n + 1) for the following values of p: 73, 83, 101, 241, 367, 653, 661.
%C A216880 n is a semiprime of the form (6*m - 1 )*(6*n - 1) for the following values of p: 107, 131, 151, 173, 397, 503, 607, 641, 683.
%C A216880 n is the square of a prime for the following values of p: 2, 17.
%C A216880 n is an absolute Fermat pseudoprime for the following value of p: 577.
%C A216880 n is a product, not squarefree, of two primes for the following values of p: 283, 311.
%C A216880 Note: any number from the sequence is a term of one of the categories above.
%C A216880 This sequence is infinite under Dickson's conjecture. - _Charles R Greathouse IV_, Sep 20 2012
%H A216880 Marius A. Burtea, <a href="/A216880/b216880.txt">Table of n, a(n) for n = 1..18020</a>
%t A216880 3#-2&/@Select[Prime[Range[200]],PrimeQ[6#+1]&] (* _Harvey P. Dale_, Mar 04 2023 *)
%o A216880 (PARI) is(n)=n%3==1 && isprime(n\3+1) && isprime(2*n+5) \\ _Charles R Greathouse IV_, Dec 07 2014
%o A216880 (MATLAB) p=primes(10000);
%o A216880 m=1;
%o A216880 for  u=1:1000
%o A216880     if  isprime(6*p(u)+1)==1
%o A216880         sol(m)=3*p(u)-2;
%o A216880         m=m+1;
%o A216880     end
%o A216880 end
%o A216880 sol % _Marius A. Burtea_, Apr 10 2019
%o A216880 (Magma) [3*p-2:p in PrimesUpTo(1000)| IsPrime(6*p+1)]; // _Marius A. Burtea_, Apr 10 2019
%K A216880 nonn
%O A216880 1,1
%A A216880 _Marius Coman_, Sep 19 2012
%E A216880 a(1) added, comment corrected by _Paolo P. Lava_, Dec 18 2012
%E A216880 Missing term 697 added by _Marius A. Burtea_, Apr 10 2019