A383243 Primes of the form p(k)*p(k+1)*(p(k+1) - p(k)) - 1 sorted by increasing k.

5, 29, 307, 883, 1747, 4001, 6067, 26227, 108883, 152083, 424481, 311347, 396883, 848201, 580627, 1713709, 1814509, 864883, 5092973, 3046789, 3386989, 1664083, 2581961, 2196307, 2304307, 2377747, 6955309, 3526867, 4088467, 20916053, 4796083, 7339361

Offset

1,1

Comments

Conjecture: there are infinitely many such primes.

Links

Table of n, a(n) for n=1..32.

Maple

q:= 2; R:= NULL: count:= 0:
while count < 100 do
  p:= q;
  q:= nextprime(q);
  v:= p*q*(q-p)-1;
  if isprime(v) then R:= R, v; count:= count+1 fi;
od:
R; # Robert Israel, May 11 2025

Mathematica

z = 200; p[n_] := Prime[n];
f[n_] := p[n]*p[n + 1]*(p[n + 1] - p[n])
t1 = Table[f[n] - 1, {n, 1, z}];    (* A383241 *)
t2 = Table[f[n] + 1, {n, 1, z}];    (* A383242 *)
Select[t1, PrimeQ[#] &]  (* A383243 *)
Select[t2, PrimeQ[#] &]  (* A383244 *)

Crossrefs

Cf. A000042, A383242, A383244.

Primes in A383241.

Sequence in context: A332469 A112799 A020531 * A195228 A226668 A226666

Adjacent sequences: A383240 A383241 A383242 * A383244 A383245 A383246

Keyword

nonn

Author

Clark Kimberling, May 07 2025

Status

approved