A103614 Semiprimes of the form prime(n)*prime(n+1)*prime(n+2) - 1.

4198, 33262, 1564258, 6672202, 7566178, 18181978, 20193022, 178433278, 187466722, 229580146, 293158126, 467821918, 1125878062, 1341880018, 4317369778, 5198554618, 8493529942, 10138087306, 10594343758, 20940647698

Offset

1,1

Comments

This is the three-consecutive-prime minus one equivalent of A103533, which is Giovanni Teofilatto's two-consecutive-prime minus one sequence.

Links

Table of n, a(n) for n=1..20.

Example

n: prime(n) * prime(n+1) * prime(n+2) - 1
6: 13 *17 *19 - 1 = 4198 = 2 * 2099
10: 29 * 31 * 37 - 1 = 33262 = 2 * 16631
29: 109 * 113 * 127 - 1 = 1564258 = 2 * 782129
42: 181 * 191 * 193 -1 = 6672202 = 2 * 3336101
44: 193 * 197 * 199 -1 = 7566178 = 2 * 3783089
55: 257 * 263 * 269 -1 = 18181978 = 2 * 9090989
57: 269 * 271 * 277 -1 = 20193022 = 2 * 10096511
102: 557 * 563 * 569 -1 = 178433278 = 2 * 89216639

Mathematica

Bigomega[n_]:=Plus@@Last/@FactorInteger[n]; SemiprimeQ[n_]:=Bigomega[n]==2; Select[Table[Prime[n]*Prime[n+1]*Prime[n+2]-1, {n, 1000}], SemiprimeQ] (* Ray Chandler, Mar 29 2005 *)

Prog

(PARI) for(n=1, 420, if(bigomega(k=prime(n)*prime(n+1)*prime(n+2)-1)==2, print1(k, ", "))) (Brockhaus)

Crossrefs

Cf. A000040, A001358, A006881, A103533, A103746, A104874, A104875.

Sequence in context: A234723 A152511 A252316 * A210330 A020438 A002241

Adjacent sequences: A103611 A103612 A103613 * A103615 A103616 A103617

Keyword

easy,nonn

Author

Jonathan Vos Post, Mar 24 2005

Extensions

Extended by Ray Chandler and Klaus Brockhaus, Mar 29 2005

Status

approved