%I #5 Nov 30 2020 15:13:14
%S 3,13,17,29
%N Primes p such that A001414(p-1)*A001414(p+1) == q (mod p), where q is the prime before p.
%C Next term, if any, > 2*10^8.
%F a(n) = prime(k) where A339327(k) = prime(k-1).
%e a(3)=17 is in the sequence because it is prime and A001414(16)*A001414(18) = 8*8 = 64 == 13 (mod 17), and 13 is the prime before 17.
%p spf:= n -> add(t[1]*t[2],t=ifactors(n)[2]):
%p p:= 1: R:= NULL:
%p while p < 10^7 do
%p q:= p: p:= nextprime(p);
%p v:= spf(p-1)*spf(p+1) mod p;
%p if v = q then R:= R, p fi
%p od:
%p R;
%Y Cf. A001414, A339327
%K nonn,bref,more
%O 1,1
%A _Robert Israel_, Nov 30 2020