%I #15 Jul 07 2024 19:17:35

%S 47,139,167,257,421,557,587,647,1021,1051,1217,1601,1759,2957,3803,

%T 3911,4007,4397,4423,4463,5351,5471,6257,6691,6857,6949,7577,8081,

%U 9109,9697,10223,10847,11927,12101,12601,12911,13669,13711,13751,14537,14621,16217,16607,16903,17021,17359,17477,17911

%N First of four consecutive primes p, q, r, s where q*s == p (mod r).

%C Prime(i) is a term if A001223(i+1)*A001223(i+2) = A001223(i) + A001223(i+1).

%H Robert Israel, <a href="/A355727/b355727.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3) = 167 is a term because 167, 173, 179, 181 are consecutive primes with 173*181 == 167 (mod 179).

%p p2:= 2: p3:= 3: p4:=5: count:= 0: R:= NULL:

%p while count < 100 do

%p p1:= p2; p2:= p3; p3:= p4; p4:= nextprime(p4);

%p if p2*p4 -p1 mod p3 = 0 then

%p count:= count+1;

%p R:= R, p1;

%p fi;

%p od:

%p R;

%Y Cf. A001223.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Jul 15 2022