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Primes p such that either x divides y, or y divides x, where x = nextprime(p) - p, and y = p - prevprime(p).
2

%I #11 May 22 2014 12:25:30

%S 3,5,7,11,13,17,19,29,31,41,43,53,59,61,71,73,97,101,103,107,109,137,

%T 139,149,151,157,173,179,181,191,193,197,199,211,223,227,229,239,241,

%U 257,263,269,271,281,283,311,313,347,349,373,397,401,419,421,431,433,457

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

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

%H Harvey P. Dale, <a href="/A239879/b239879.txt">Table of n, a(n) for n = 1..1000</a>

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

%t 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 *)

%o (Python)

%o import sympy

%o prpr = 2

%o prev = 3

%o for i in range(5,1000,2):

%o if sympy.isprime(i):

%o x = i - prev

%o y = prev - prpr

%o if x%y==0 or y%x==0: print str(prev)+',',

%o prpr = prev

%o prev = i

%Y Cf. A000040, A239584.

%K nonn

%O 1,1

%A _Alex Ratushnyak_, Mar 28 2014