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

A104875 Semiprimes of the form prime(n)*prime(n+1)*prime(n+2)*prime(n+3)*prime(n+4) - 1.

Original entry on oeis.org

15014, 1062346, 600662302, 2224636919002, 118335570521086, 168652154886862, 3790374062238502, 6290838589498366, 127018534712243098, 131125107904515418, 190740905520325018, 2057351971883521282, 3151949824862998762
Offset: 1

Views

Author

Jonathan Vos Post, Mar 29 2005

Keywords

Comments

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

Examples

			n prime(n) * prime(n+1) * prime(n+2) * prime(n+3) * prime(n+4) - 1
1: 2 * 3 * 5 * 7 * 11 - 1 = 2309 is prime; examples hereafter are semiprime
2: 3 * 5 * 7 * 11 * 13 - 1 = 15014 = 2 * 7507
5: 11 * 13 * 17 * 19 * 23 - 1 = 1062346 = 2 * 531173
15: 47 * 53 * 59 * 61 * 67 - 1 = 600662302 = 2 * 300331151
60: 281 * 283 * 293 * 307 * 311 - 1 = 2224636919002 = 2 * 1112318459501
117: 643 * 647 * 653 * 659 * 661 - 1 = 118335570521086 = 2 * 59167785260543

Links

Crossrefs

Cf. A000040, A001358, A006881, A103533, A103614, A103746, A104874.

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]*Prime[n+4]-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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