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

Author

N. J. A. Sloane

Keywords

• nonn

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)

Crossrefs

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

A278583 is an equivalent sequence.

See also A278585.

Programs

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 *)

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