%I
%S 1,2,4,90,2397,3207,3948,8033,8851,15596,20173,21156,23870,24262,
%T 24863,25279,26217,26913,27967,30079,31329,41193,41894,43871,45154,
%U 45719,46385,47142,49128,50081,53652,57882,58281,61508,61955,63084,68685,74615,75291,75522,77412,78717,80960,81997,88931
%N Numbers k such that prime(k+1)^prime(k+3) == prime(k) mod prime(k+2).
%C The prime ktuples conjecture implies that there are infinitely many k for which prime(k) to prime(k+3) are of the form p32, p2, p, p+4, and then (p2)^(p+4) == (2)^5 == p32 (mod p).
%H Robert Israel, <a href="/A335571/b335571.txt">Table of n, a(n) for n = 1..5000</a>
%e Prime(4) to prime(7) are 7, 11, 13, 17, and 11^17 == 7 (mod 13), so a(3)=4 is in the sequence.
%p q:= 2: r:= 3: s:= 5: R:= NULL: count:= 0:
%p for k from 1 while count < 100 do
%p p:= q; q:= r; r:= s; s:= nextprime(s);
%p if q&^s  p mod r = 0 then count:= count+1; R:= R, k; fi
%p od:
%p R;
%Y Cf. A340868.
%K nonn
%O 1,2
%A _J. M. Bergot_ and _Robert Israel_, Jan 26 2021
