A118624 Primes of the form prime(n+1)*prime(n+3) - prime(n)*prime(n+2) - 1, ordered by n.

59, 359, 197, 719, 449, 971, 1019, 937, 419, 863, 809, 2203, 1979, 1693, 743, 2693, 3169, 1823, 3119, 1637, 2239, 4547, 4241, 4967, 4877, 4259, 2609, 5651, 7759, 7823, 4219, 8971, 6863, 6983, 7451, 3989, 12161, 8147, 11423, 10369, 9059, 3299, 6863

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Maple

P:=proc(n)local i, j; for i from 1 by 1 to n do j:=abs(ithprime(i)*ithprime(i+2)-ithprime(i+1)*ithprime(i+3))-1; if isprime(j) then print(j); fi; od; end: P(1000);

Mathematica

s=Table[Prime[n+1]*Prime[n+3] - Prime[n]*Prime[n+2] - 1, {n, 147}]; Select[s, PrimeQ] (* James C. McMahon, Sep 16 2024 *)
Select[#[[2]]#[[4]]-#[[1]]#[[3]]-1&/@Partition[Prime[Range[300]], 4, 1], PrimeQ] (* Harvey P. Dale, Oct 05 2024 *)

Prog

(PARI) my(v=List(), p=2, q=3, r=5); forprime(s=7, 1e6, my(t=q*s-p*r-1); if(ispseudoprime(t), listput(v, t)); p=q; q=r; r=s); v=Vec(v) \\ Charles R Greathouse IV, Feb 17 2011

Crossrefs

Cf. A117854.

Sequence in context: A033238 A142265 A290183 * A244772 A142604 A071771

Adjacent sequences: A118621 A118622 A118623 * A118625 A118626 A118627

Keyword

nonn,easy

Author

Paolo P. Lava and Giorgio Balzarotti, May 09 2006

Extensions

Definition clarified by Charles R Greathouse IV, Feb 17 2011

Status

approved