cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

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

Original entry on oeis.org

4198, 33262, 1564258, 6672202, 7566178, 18181978, 20193022, 178433278, 187466722, 229580146, 293158126, 467821918, 1125878062, 1341880018, 4317369778, 5198554618, 8493529942, 10138087306, 10594343758, 20940647698
Offset: 1

Views

Author

Jonathan Vos Post, Mar 24 2005

Keywords

Comments

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

Examples

			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

Links

Crossrefs

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

Programs

  • 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 *)
Select[Times@@#-1&/@Partition[Prime[Range[500]],3,1],PrimeOmega[#]==2&] (* Harvey P. Dale, Mar 03 2025 *)
  • PARI
    for(n=1,420,if(bigomega(k=prime(n)*prime(n+1)*prime(n+2)-1)==2,print1(k,","))) (Brockhaus)

Extensions

Extended by Ray Chandler and Klaus Brockhaus, Mar 29 2005

A104874 Semiprimes of the form prime(n)*prime(n+1)*prime(n+2)*prime(n+3) - 1.

Original entry on oeis.org

209, 1154, 645328246, 2445956098, 2337448622686, 19317973275826, 22894376863198, 32220239865718, 51087435019342, 78382834887262, 163068083613646, 176031800345938, 622751201209726, 1292966939911018
Offset: 1

Views

Author

Jonathan Vos Post, Mar 29 2005

Keywords

Comments

This is the four-consecutive-prime minus one equivalent of A103533.

Examples

			n: prime(n) * prime(n+1) * prime(n+2) * prime(n+3) - 1
1: 2 * 3 * 5 * 7 - 1 = 209 = 11 * 19
2: 3 * 5 * 7 * 11 - 1 = 1154 = 2 * 577
36: 151 * 157 * 163 * 167 - 1 = 645328246 = 2 * 322664123
47: 211 * 223 * 227 * 229 - 1 = 2445956098 = 2 * 1222978049
201: 1229 * 1231 * 1237 * 1249 - 1 = 2337448622686 = 2 * 1168724311343.

Links

Crossrefs

Cf. A000040, A001358, A006881, A103533, A103614, A103746, A104875.

Programs

  • Mathematica
    Bigomega[n_]:=Plus@@Last/@FactorInteger[n]; SemiprimeQ[n_]:=Bigomega[n]==2; Select[Table[Prime[n]*Prime[n+1]*Prime[n+2]*Prime[n+3]-1, {n, 1000}], SemiprimeQ] (* Ray Chandler, Mar 29 2005 *)

Extensions

Extended by Ray Chandler, Mar 29 2005
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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