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A058620 Lesser of two consecutive primes whose difference divided by two is a prime: ( prime(next prime after n) - prime(n) )/2 is prime.

%I A058620 #19 Jan 20 2021 17:22:53
%S A058620 7,13,19,23,31,37,43,47,53,61,67,73,79,83,97,103,109,113,127,131,139,
%T A058620 151,157,163,167,173,181,193,223,229,233,241,251,257,263,271,277,283,
%U A058620 293,307,313,317,331,337,349,353,367,373,379,383,397,409,421,433,439
%N A058620 Lesser of two consecutive primes whose difference divided by two is a prime: ( prime(next prime after n) - prime(n) )/2 is prime.
%C A058620 Lesser of two consecutive primes whose difference is a semiprime (A001358). - _Zak Seidov_, Nov 19 2016
%H A058620 Charles R Greathouse IV, <a href="/A058620/b058620.txt">Table of n, a(n) for n = 1..10000</a>
%t A058620 Do[ If[ PrimeQ[ (Prime[n + 1] - Prime[n] )/2], Print[ Prime[n] ]], {n, 1, 100} ]
%t A058620 p=7;Reap[Do[If[PrimeQ[((q=NextPrime[p])-p)/2],Sow[p]];p=q,{100}]][[2, 1]] (* _Zak Seidov_, Nov 19 2016 *)
%t A058620 Select[Partition[Prime[Range[100]],2,1],PrimeQ[(#[[2]]-#[[1]])/2]&][[All,1]] (* _Harvey P. Dale_, Jan 20 2021 *)
%o A058620 (PARI) isok(p) = isprime(p) && isprime((nextprime(p+1) - p)/2); \\ _Michel Marcus_, Nov 19 2016
%o A058620 (PARI) v=List(); p=3; forprime(q=5,, if(isprime((q-p)/2), listput(v,p); if(#v==10^4, return)); p=q) \\ _Charles R Greathouse IV_, Nov 20 2016
%Y A058620 Cf. A001358.
%K A058620 nonn
%O A058620 1,1
%A A058620 _Robert G. Wilson v_, Dec 28 2000