A209617 Primes separated from their adjacent primes on both sides by a prime number of successive composites.

23, 37, 47, 53, 67, 79, 83, 89, 97, 113, 127, 131, 157, 163, 167, 173, 211, 223, 233, 257, 263, 277, 307, 317, 331, 353, 359, 367, 373, 379, 383, 389, 397, 401, 439, 443, 449, 457, 467, 479, 487, 491, 499, 503, 509, 541, 563, 593, 607, 613, 647, 653, 673, 677

Offset

1,1

Comments

Intersection of A209623 and A209624.

Links

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

Example

a(1)=23 is the first prime separated both from its previous prime neighbor (19) and next prime neighbor (29) by a prime number (respectively 3 and 5) of composites: [19], 20, 21, 22, [23], 24, 25, 26, 27, 28, [29].

Mathematica

d = Differences[Prime[Range[200]]] - 1; t = {}; Do[If[PrimeQ[d[[i - 1]]] && PrimeQ[d[[i]]], AppendTo[t, Prime[i]]], {i, 2, Length[d]}]; t (* T. D. Noe, Mar 18 2012 *)

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), listput(v, q)); p=q; q=r); Vec(v) \\ Charles R Greathouse IV, Apr 30 2016

Crossrefs

Cf. A209623, A209624.

Sequence in context: A173829 A110673 A134797 * A179780 A153740 A055114

Adjacent sequences: A209614 A209615 A209616 * A209618 A209619 A209620

Keyword

nonn

Author

Lekraj Beedassy, Mar 12 2012

Status

approved