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A350460 Positive integers k such that if p is the next prime > k then p - k is prime.

%I A350460 #18 Jan 12 2022 21:42:25
%S A350460 3,5,8,9,11,14,15,17,20,21,24,26,27,29,32,34,35,38,39,41,44,45,48,50,
%T A350460 51,54,56,57,59,62,64,65,68,69,71,74,76,77,80,81,84,86,87,90,92,94,95,
%U A350460 98,99,101,104,105,107,110,111,114,116,120,122,124,125,128,129
%N A350460 Positive integers k such that if p is the next prime > k then p - k is prime.
%C A350460 a(n) is only prime when n is the lesser of a twin prime pair (A001359). All other terms are composite.
%e A350460 3 is a term because the next prime > 3 is 5, and 5 - 3 = 2, which is prime.
%e A350460 14 is a term because the next prime > 14 is 17, and 17 - 14 = 3, which is prime.
%t A350460 Select[Range[130], PrimeQ[NextPrime[#] - #] &] (* _Amiram Eldar_, Jan 01 2022 *)
%o A350460 (Python)
%o A350460 from sympy import isprime, nextprime
%o A350460 def ok(n): return n > 0 and isprime(nextprime(n) - n)
%o A350460 print([k for k in range(130) if ok(k)]) # _Michael S. Branicky_, Jan 01 2022
%o A350460 (PARI) isok(k) = my(p=nextprime(k+1)); isprime(p-k); \\ _Michel Marcus_, Jan 01 2022
%Y A350460 Cf. A038711, A001359, A068780.
%K A350460 nonn
%O A350460 1,1
%A A350460 _Ryan Bresler_, Jan 01 2022