A355485 - OEIS

%I #11 Jul 13 2022 07:18:13

%S 1327,2477,3137,5531,8467,9973,11213,11743,12011,12163,12347,14897,

%T 16007,16493,16703,17257,19087,20297,20443,21433,24443,26267,26513,

%U 29033,29501,29683,31193,31907,32653,32843,34549,34781,35543,35771,36161,36497,36947,37061,37747,38993,39581,40361,40433

%N Primes p such that neither g-1 nor g+1 is prime, where g is the gap from p to the next prime.

%C Primes prime(i) where A001223(i) is in A061673.

%H Robert Israel, <a href="/A355485/b355485.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 3137 is a term because 3137 is prime, the next prime is 3163 = 3137+26, and neither 26-1 = 25 nor 26+1 = 27 is prime.

%p q:= 2:

%p count:= 0:

%p R:= NULL:

%p while count < 100 do

%p   p:= q;

%p   q:= nextprime(q);

%p   g:= q-p;

%p   if not(isprime(g-1) or isprime(g+1)) then

%p      count:= count+1;

%p      R:= R, p

%p   fi

%p od:

%p R;

%o (PARI) isok(p) = if (isprime(p), my(g=nextprime(p+1)-p); !isprime(g-1) && !isprime(g+1)); \\ _Michel Marcus_, Jul 05 2022

%Y Cf. A001223, A061673.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Jul 04 2022