A390797 Primes of the form (p*q*r - p - q - r)/2, where p, q, r are consecutive primes.

181, 6301, 23459, 95287, 120473, 291661, 1418491, 1563461, 3335819, 4135613, 9585817, 10546499, 17679707, 39283499, 42103613, 61619017, 93732503, 96697697, 185300681, 269327419, 287600821, 379672913, 417491587, 553277897, 572746661, 771708661, 972583811, 1028149741, 1089212819, 1192892039

Offset

1,1

Comments

For odd numbers p, q, r, p*q*r - p - q - r == 2 (mod 4).

Links

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

Example

a(3) = 23459 = (31*37*41 - 31 - 37 - 41)/2 where 31, 37 and 41 are consecutive primes, and 23459 is prime.

Maple

P:= select(isprime, [seq(i, i=3..10^4, 2)]):
select(isprime, [seq((P[i]*P[i+1]*P[i+2]-P[i]-P[i+1]-P[i+2])/2, i=1..nops(P)-2)]);

Mathematica

s={}; Do[p=Prime[j]; q=NextPrime[p]; r=NextPrime[p, 2]; If[PrimeQ[(p*q*r-p-q-r)/2], AppendTo[s, (p*q*r-p-q-r)/2]], {j, 216}]; s (* James C. McMahon, Nov 25 2025 *)

Crossrefs

Cf. A096342, A390796.

Sequence in context: A155018 A179814 A293655 * A008379 A262141 A212938

Adjacent sequences: A390794 A390795 A390796 * A390798 A390799 A390800

Keyword

nonn

Author

Will Gosnell and Robert Israel, Nov 19 2025

Status

approved