A087714 - OEIS

%I #9 May 05 2021 11:01:45

%S 5,13,19,367

%N Primes p = prime(i) such that p(i)# - p(i+1) and p(i)# + p(i+1) are both primes, where p# = A002110.

%C Conjecture: there are only 4 primes in this sequence.

%e 2*3*5-7 = 23 is prime, 2*3*5+7 = 37 is prime.

%o (PARI) isok(p) = {if (isprime(p), my(pp = prod(k=1, primepi(p), prime(k)), q = nextprime(p+1)); isprime(pp-q) && isprime(pp+q););} \\ _Michel Marcus_, Sep 20 2019

%o (PARI) my(pr=1); forprime(p=1, , pr=pr*p; if(ispseudoprime(pr-nextprime(p+1)) && ispseudoprime(pr+nextprime(p+1)), print1(p, ", "))) \\ _Felix Fröhlich_, Sep 20 2019

%Y Cf. A087715, A087716, A087728.

%Y Cf. A002110.

%K nonn,more

%O 1,1

%A _Pierre CAMI_, Sep 28 2003