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 1-3 of 3 results.

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

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

A103767 Numbers n such that prime(n)*prime(n+1)*prime(n+2) - 1 is semiprime.

Original entry on oeis.org

6, 10, 29, 42, 44, 55, 57, 102, 104, 111, 120, 136, 174, 184, 257, 269, 308, 325, 327, 401, 426, 504, 514, 565, 571, 594, 595, 652, 717, 755, 864, 882, 901, 907, 985, 1014, 1074, 1134, 1141, 1156, 1198, 1301, 1327, 1346, 1362, 1654, 1670, 1674, 1778, 1897
Offset: 1

Views

Author

Klaus Brockhaus, Mar 29 2005

Keywords

Examples

			prime(10)*prime(11)*prime(12) - 1 = 29*31*37 - 1 = 33262= 2*16631, hence 10 is
a term.

Links

Crossrefs

Cf. A001358, A006881, A103614, A103746.

Programs

  • Mathematica
    PrimePi/@Transpose[Select[Partition[Prime[Range[2000]],3,1], PrimeOmega[ Times@@#-1]==2&]][[1]] (* Harvey P. Dale, Mar 15 2015 *)
  • PARI
    for(n=1,1900,if(bigomega(prime(n)*prime(n+1)*prime(n+2)-1)==2,print1(n,",")))
Showing 1-3 of 3 results.

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

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