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 A036570 Primes p such that (p+1)/2 and (p+2)/3 are also primes. 8

%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%3-1) & 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.