%I
%S 13,37,157,541,877,1201,1381,1621,2017,2557,2857,3061,4357,4441,5077,
%T 5581,5701,6337,6637,6661,6997,7417,8221,9181,9661,9901,10837,11497,
%U 12457,12601,12721,12757,13681,14437,15241,16921,17077,18217
%N Primes p such that (p+1)/2 and (p+2)/3 are also primes.
%C The prime p is followed by two semiprimes; a third semiprime is not possible.  _T. D. Noe_, Jul 23 2008
%C A subsequence of A005383, which has A163573 as a subsequence.  _M. F. Hasler_, Feb 26 2012
%C Similarly, the only "prime sandwiched by semiprimes" is 5.  _Zak Seidov_, Aug 04 2013
%C 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
%C All terms are congruent to 1 mod 12.  _Zak Seidov_, Feb 16 2017
%H T. D. Noe, <a href="/A036570/b036570.txt">Table of n, a(n) for n=1..1000</a>
%t 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 *)
%o (PARI) is_A036570(n)={ !(n%31) & isprime(n\3+1) & isprime(n\2+1) & isprime(n) }
%o for(n=1,2e4,is_A036570(n) & print1(n",")) \\ _M. F. Hasler_, Feb 26 2012
%Y Cf. A005383, A074200, A093553, A147615, A163573.
%Y A278583 is an equivalent sequence.
%Y See also A278585.
%K nonn
%O 1,1
%A _N. J. A. Sloane_
