A272367 Primes p separated from their adjacent primes on both sides by a prime number of successive composites, while the adjacent primes of p are separated by a prime number of integers.

53, 89, 97, 113, 127, 157, 173, 211, 257, 263, 307, 317, 331, 359, 367, 373, 389, 397, 401, 449, 457, 479, 487, 491, 499, 509, 541, 563, 593, 607, 653, 683, 727, 733, 743, 751, 761, 769, 773, 853, 863, 877, 887, 907, 911, 937, 947, 953, 967, 977, 983, 991, 997, 1069, 1103, 1109, 1117, 1123, 1187

Offset: 1

Author

Marc Morgenegg, Apr 27 2016

Keywords

• nonn

Examples

			a(1) = 53. The primes around and including 53 are {47, 53, 59}. The number of composites between these are {5, 5} and the number of integers between 47 and 59 is 11; all of {5, 5, 11} are prime, thus 53 is a term.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A209617.

Programs

Mathematica

Select[Prime@ Range@ 195, Function[p, Times @@ Boole@ PrimeQ@ Flatten[Map[Differences, {#, Delete[#, 2]}] - 1] &@ Map[NextPrime[p, #] &, Range[-1, 1]] == 1]] (* Michael De Vlieger, Apr 27 2016 *)

PARI

list(lim)=my(v=List(),p=2,q=3); forprime(r=5,nextprime(lim\1+1), if(isprime(q-p-1) && isprime(r-q-1) && isprime(r-p-1), listput(v,q)); p=q; q=r); Vec(v) \\ Charles R Greathouse IV, Apr 30 2016

Extensions

More terms from Michael De Vlieger, Apr 27 2016