

A335571


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


1



1, 2, 4, 90, 2397, 3207, 3948, 8033, 8851, 15596, 20173, 21156, 23870, 24262, 24863, 25279, 26217, 26913, 27967, 30079, 31329, 41193, 41894, 43871, 45154, 45719, 46385, 47142, 49128, 50081, 53652, 57882, 58281, 61508, 61955, 63084, 68685, 74615, 75291, 75522, 77412, 78717, 80960, 81997, 88931
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OFFSET

1,2


COMMENTS

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).


LINKS

Robert Israel, Table of n, a(n) for n = 1..5000


EXAMPLE

Prime(4) to prime(7) are 7, 11, 13, 17, and 11^17 == 7 (mod 13), so a(3)=4 is in the sequence.


MAPLE

q:= 2: r:= 3: s:= 5: R:= NULL: count:= 0:
for k from 1 while count < 100 do
p:= q; q:= r; r:= s; s:= nextprime(s);
if q&^s  p mod r = 0 then count:= count+1; R:= R, k; fi
od:
R;


CROSSREFS

Cf. A340868.
Sequence in context: A018410 A270484 A327427 * A335291 A156496 A007534
Adjacent sequences: A335568 A335569 A335570 * A335572 A335573 A335574


KEYWORD

nonn


AUTHOR

J. M. Bergot and Robert Israel, Jan 26 2021


STATUS

approved



