A239879 Primes p such that either x divides y, or y divides x, where x = nextprime(p) - p, and y = p - prevprime(p).

3, 5, 7, 11, 13, 17, 19, 29, 31, 41, 43, 53, 59, 61, 71, 73, 97, 101, 103, 107, 109, 137, 139, 149, 151, 157, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 239, 241, 257, 263, 269, 271, 281, 283, 311, 313, 347, 349, 373, 397, 401, 419, 421, 431, 433, 457

Offset: 1

Author

Alex Ratushnyak, Mar 28 2014

Keywords

• nonn

Comments

x and y are the distances from p to the nearest primes above and below p.

Examples

			The distances from p=29 to two nearest primes are 6 and 2, and, because 2 divides 6, p=29 is in the sequence.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A239584.

Programs

Mathematica

divQ[n_]:=Module[{pr=n-NextPrime[n,-1],nx=NextPrime[n]-n},Divisible[ pr,nx]||Divisible[nx,pr]]; Select[Prime[Range[2,100]],divQ] (* Harvey P. Dale, May 22 2014 *)

Python

import sympy
prpr = 2
prev = 3
for i in range(5,1000,2):
    if sympy.isprime(i):
        x = i - prev
        y = prev - prpr
        if x%y==0 or y%x==0: print(prev, end=', ')
        prpr = prev
        prev = i