login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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
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
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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