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

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

Offset

1,2

Comments

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).

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