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A335571 Numbers k such that prime(k+1)^prime(k+3) == prime(k) mod prime(k+2). 1

%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 k-tuples conjecture implies that there are infinitely many k for which prime(k) to prime(k+3) are of the form p-32, p-2, p, p+4, and then (p-2)^(p+4) == (-2)^5 == p-32 (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

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Last modified July 27 13:36 EDT 2021. Contains 346306 sequences. (Running on oeis4.)