

A036570


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


8



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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

T. D. Noe, Table of n, a(n) for n=1..1000


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%31) & 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 A298683 A173872
Adjacent sequences: A036567 A036568 A036569 * A036571 A036572 A036573


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


STATUS

approved



