A036570 Primes p such that (p+1)/2 and (p+2)/3 are also primes.

13, 37, 157, 541, 877, 1201, 1381, 1621, 2017, 2557, 2857, 3061, 4357, 4441, 5077, 5581, 5701, 6337, 6637, 6661, 6997, 7417, 8221, 9181, 9661, 9901, 10837, 11497, 12457, 12601, 12721, 12757, 13681, 14437, 15241, 16921, 17077, 18217

Offset

1,1

Comments

The prime p is followed by two semiprimes; a third semiprime is not possible. - T. D. Noe, Jul 23 2008

A subsequence of A005383, which has A163573 as a subsequence. - M. F. Hasler, Feb 26 2012

Similarly, the only "prime sandwiched by semiprimes" is 5. - Zak Seidov, Aug 04 2013

For n > 1, a(n) == 1 or (7 mod 10). If a(n) == 3 (mod 10), then (a(n) + 2)/3 == 0 (mod 5) which is a composite number if a(n) > 13. - Chai Wah Wu, Nov 30 2016

All terms are congruent to 1 (mod 12). - Zak Seidov, Feb 16 2017

Links

Jon E. Schoenfield, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)

Mathematica

lst={}; Do[p=Prime[n]; If[PrimeQ[(p+1)/2]&&PrimeQ[(p+2)/3], AppendTo[lst, p]], {n, 8!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 31 2009 *)

Prog

(PARI) is_A036570(n)={ !(n%3-1) & isprime(n\3+1) & isprime(n\2+1) & isprime(n) }
for(n=1, 2e4, is_A036570(n) & print1(n", "))  \\ M. F. Hasler, Feb 26 2012

Crossrefs

Cf. A005383, A074200, A093553, A147615, A163573.

A278583 is an equivalent sequence.

See also A278585.

Sequence in context: A155903 A139860 A201480 * A147615 A371512 A298683

Adjacent sequences: A036567 A036568 A036569 * A036571 A036572 A036573

Keyword

nonn

Author

N. J. A. Sloane

Status

approved