A111071 Difference between the product of two consecutive primes and the next prime.

1, 8, 24, 64, 126, 202, 300, 408, 636, 862, 1106, 1474, 1716, 1968, 2432, 3066, 3532, 4016, 4684, 5104, 5684, 6468, 7290, 8532, 9694, 10296, 10912, 11550, 12190, 14220, 16500, 17808, 18894, 20560, 22342, 23544, 25424, 27048, 28712, 30786, 32208

Offset: 1

Author

Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Oct 09 2005

Keywords

• nonn

Examples

			a(4)= prime(4)*prime(5)-prime(6) = 7*11-13=64.
		

Crossrefs

Cf. A000040.

Programs

Magma

[NthPrime(n)*NthPrime(n+1)-NthPrime(n+2): n in [1..50]]; // Vincenzo Librandi, Jul 18 2015

Maple

seq(ithprime(n)*ithprime(n+1)-ithprime(n+2), n=1..50); # Emeric Deutsch, Oct 10 2005

Mathematica

f[n_] := Prime[n]Prime[n + 1] - Prime[n + 2]; Table[ f[n], {n, 41}] (* Robert G. Wilson v, Oct 10 2005  *)
#[[1]]*#[[2]]-#[[3]]&/@Partition[Prime[Range[50]],3,1] (* Harvey P. Dale, Aug 06 2015 *)

PARI

main(size)=my(n);vector(size,n,prime(n)*prime(n+1)-prime(n+2)) /* Anders Hellström, Jul 16 2015 */

Formula

a(n) = prime(n)*prime(n+1)-prime(n+2) = A006094(n)-A000040(n+2) = 2*A152527(n-1).

Extensions

More terms from Robert G. Wilson v and Emeric Deutsch, Oct 10 2005