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 A216880 Numbers of the form 3p - 2 where p and 6p + 1 are prime. 1
 4, 7, 13, 19, 31, 37, 49, 67, 109, 139, 181, 217, 247, 301, 307, 319, 391, 409, 451, 517, 541, 697, 721, 769, 787, 811, 829, 847, 877, 931, 937, 991, 1039, 1099, 1117, 1189, 1327, 1381, 1399, 1507, 1669, 1729, 1777, 1801, 1819, 1921, 1957, 1981, 2047, 2179, 2251, 2281 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This formula produces many primes and semiprimes. Taken just the terms from the sequence above: 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. 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. 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. n is the square of a prime for the following values of p: 2, 17. n is an absolute Fermat pseudoprime for the following value of p: 577. n is a product, not squarefree, of two primes for the following values of p: 283, 311. Note: any number from the sequence is a term of one of the categories above. This sequence is infinite under Dickson's conjecture. - Charles R Greathouse IV, Sep 20 2012 LINKS Marius A. Burtea, Table of n, a(n) for n = 1..18020 MATHEMATICA 3#-2&/@Select[Prime[Range[200]], PrimeQ[6#+1]&] (* Harvey P. Dale, Mar 04 2023 *) PROG (PARI) is(n)=n%3==1 && isprime(n\3+1) && isprime(2*n+5) \\ Charles R Greathouse IV, Dec 07 2014 (MATLAB) p=primes(10000); m=1; for u=1:1000 if isprime(6*p(u)+1)==1 sol(m)=3*p(u)-2; m=m+1; end end sol % Marius A. Burtea, Apr 10 2019 (Magma) [3*p-2:p in PrimesUpTo(1000)| IsPrime(6*p+1)]; // Marius A. Burtea, Apr 10 2019 CROSSREFS Sequence in context: A023496 A191868 A176003 * A144730 A058570 A134781 Adjacent sequences: A216877 A216878 A216879 * A216881 A216882 A216883 KEYWORD nonn AUTHOR Marius Coman, Sep 19 2012 EXTENSIONS a(1) added, comment corrected by Paolo P. Lava, Dec 18 2012 Missing term 697 added by Marius A. Burtea, Apr 10 2019 STATUS approved

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Last modified February 27 19:16 EST 2024. Contains 370378 sequences. (Running on oeis4.)