cp's OEIS Frontend

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

%I A239879 #15 Aug 07 2025 15:03:09
%S A239879 3,5,7,11,13,17,19,29,31,41,43,53,59,61,71,73,97,101,103,107,109,137,
%T A239879 139,149,151,157,173,179,181,191,193,197,199,211,223,227,229,239,241,
%U A239879 257,263,269,271,281,283,311,313,347,349,373,397,401,419,421,431,433,457
%N A239879 Primes p such that either x divides y, or y divides x, where x = nextprime(p) - p, and y = p - prevprime(p).
%C A239879 x and y are the distances from p to the nearest primes above and below p.
%H A239879 Harvey P. Dale, <a href="/A239879/b239879.txt">Table of n, a(n) for n = 1..1000</a>
%e A239879 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 A239879 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 A239879 (Python)
%o A239879 import sympy
%o A239879 prpr = 2
%o A239879 prev = 3
%o A239879 for i in range(5,1000,2):
%o A239879     if sympy.isprime(i):
%o A239879         x = i - prev
%o A239879         y = prev - prpr
%o A239879         if x%y==0 or y%x==0: print(prev, end=', ')
%o A239879         prpr = prev
%o A239879         prev = i
%Y A239879 Cf. A000040, A239584.
%K A239879 nonn
%O A239879 1,1
%A A239879 _Alex Ratushnyak_, Mar 28 2014