A360542 Primes prime(k) such that ( 9*(prime(k-1) - prime(k-2)) ) | (prime(k)^3 + 1).

5, 11, 17, 23, 47, 71, 107, 113, 131, 149, 179, 191, 197, 233, 239, 251, 269, 293, 311, 317, 353, 359, 431, 467, 479, 503, 521, 557, 647, 683, 719, 797, 809, 821, 827, 839, 857, 863, 881, 887, 947, 953, 971, 1019, 1031, 1061, 1097, 1103, 1151, 1163, 1223, 1259

Offset

1,1

Comments

All terms == 2 (mod 3). - Robert Israel, Oct 12 2025

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

11 is a term since (11^3 + 1)/(9*(7-5)) = 1332/18 = 74.
131 is a term since (131^3 + 1)/(9*(127-113)) = 2248092/126 = 17842.

Maple

R:= NULL: count:= 0:
q:= 2: r:=3:
while count < 100 do
  p:= q; q:= r; r:= nextprime(r);
  if (r^3+1) mod (9*(q-p)) = 0 then
    R:= R, r; count:= count+1
  fi
od:
R; # Robert Israel, Oct 12 2025

Mathematica

Select[Partition[Prime[Range[210]], 3, 1], Divisible[(#[[3]]^3 + 1)/9, #[[2]] - #[[1]]] &][[;; , 3]] (* Amiram Eldar, Feb 11 2023 *)

Crossrefs

Cf. A000040, A001223, A030078.

Sequence in context: A049755 A096449 A268640 * A214912 A216551 A314255

Adjacent sequences: A360539 A360540 A360541 * A360543 A360544 A360545

Keyword

nonn

Author

Najeem Ziauddin, Feb 11 2023

Status

approved