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

1,1

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Subsequence of A209617.

Sequence in context: A118149 A251144 A214230 * A119289 A124282 A137869

Adjacent sequences: A272364 A272365 A272366 * A272368 A272369 A272370

Keyword

nonn

Author

Marc Morgenegg, Apr 27 2016

Extensions

More terms from Michael De Vlieger, Apr 27 2016

Status

approved