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A036570 Primes p such that (p+1)/2 and (p+2)/3 are also primes. 7
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%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 A173872 A155241

Adjacent sequences:  A036567 A036568 A036569 * A036571 A036572 A036573

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 27 16:36 EDT 2017. Contains 284177 sequences.