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
Keywords
Examples
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].
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..10000
Programs
-
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 *) -
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
Comments