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.

Previous Showing 11-18 of 18 results.

A139197 Natural numbers of the form (prime(n)!-9)/9.

Original entry on oeis.org

559, 4435199, 691891199, 39520825343999, 13516122267647999, 2872446304320552959999, 982417999304411328282623999999, 913648739353102535302840319999999
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Crossrefs

Programs

  • Mathematica
    Table[(Prime[n]! - 9)/9, {n, 4, 20}]
    (Prime[Range[4,20]]!-9)/9 (* Harvey P. Dale, Apr 10 2019 *)

A139206 Smallest son factorial prime p of order n: smallest p such that p!/n-1 is prime.

Original entry on oeis.org

3, 3, 29, 5, 5, 5, 7, 11, 17, 5, 19, 7, 13, 7, 5, 37, 139, 19
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008, Apr 24 2008

Keywords

Comments

For smallest daughter factorial prime p of order n (smallest p such that (p!+n)/n = p!/n + 1 is prime), see A139074.
a(19) is currently unknown, a(20)=5, a(21)=7, a(22)=19.
a(19)>10000, a(23)=71, a(24)=3361. [From Andrew V. Sutherland, Apr 23 2008]
a(25)=17, a(26)=223, a(27)=157, a(28)=7, a(29)=41, a(30)=5, a(31)=31, a(32)=71, a(33)=13, a(34)=37, a(35)=19, a(36)=7, a(37)=47, a(38)=53, a(39)=13, a(40)=5, a(41)=127, a(42)=13, a(43)=67, a(44)=11, a(45)=17, a(46)=43, a(47)=71, a(48)=11, a(49)=19, a(50)=29, a(51)=17, a(52)=17, a(53)>10000.
a(19)>25000, a(53)>25000. [From Sean A. Irvine, Nov 14 2010]
a(54)=11, a(55)=23, a(56)=7, a(57)=433.
a(58)=283, a(59)>1500, a(60..66)=(7,139,239,7,11,13,13), a(67), a(68) > 1300, a(69..72)=(29,7,83,13), a(73)>1000. [From M. F. Hasler, Nov 03 2013]
Sequence A151900 (tentatively?) lists "singular indices", i.e., those for which a(n) is difficult to find. - M. F. Hasler, Nov 03 2013

Crossrefs

Programs

  • Mathematica
    a = {}; Do[k = 1; While[ ! PrimeQ[(Prime[k]! - n)/n], k++ ]; Print[a]; AppendTo[a, Prime[k]], {n, 1, 100}]; a (*Artur Jasinski*)
  • PARI
    a(n)=forprime(p=1,,p!%n==0 && ispseudoprime(p!/n-1) && return(p)) \\ - M. F. Hasler, Nov 03 2013

Extensions

Edited by M. F. Hasler, Nov 03 2013

A139200 Numbers k such that (k!-5)/5 is prime.

Original entry on oeis.org

5, 11, 12, 16, 36, 41, 42, 47, 127, 136, 356, 829, 1863, 2065, 2702, 4509, 7498
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Comments

a(16) > 3000. - Ray G. Opao, Oct 05 2008
a(18) > 25000. - Robert Price, Nov 20 2016

Crossrefs

Programs

  • Magma
    [n: n in [5..500] | IsPrime((Factorial(n)-5) div 5)]; // Vincenzo Librandi, Nov 21 2016
  • Mathematica
    a = {}; Do[If[PrimeQ[(n! - 5)/5], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a (* Artur Jasinski *)

Extensions

a(13)-a(15) from Ray G. Opao, Oct 05 2008
a(16) from Serge Batalov, Feb 18 2015
a(17) from Robert Price, Nov 20 2016

A139201 Numbers k such that (k!-6)/6 is prime.

Original entry on oeis.org

4, 5, 7, 8, 11, 14, 16, 17, 18, 20, 43, 50, 55, 59, 171, 461, 859, 2830, 3818, 5421, 5593, 10118, 10880, 24350
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Comments

a(25) > 25000. - Robert Price, Dec 15 2016

Crossrefs

Programs

  • Maple
    a:=proc(n) if isprime((1/6)*factorial(n)-1)=true then n else end if end proc: seq(a(n),n=4..500); # Emeric Deutsch, Apr 29 2008
  • Mathematica
    a = {}; Do[If[PrimeQ[(n! - 6)/6], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a (* Artur Jasinski *)

Extensions

2 more terms from Emeric Deutsch, Apr 29 2008
More terms from Serge Batalov, Feb 18 2015
a(22)-a(24) from Robert Price, Dec 15 2016

A139202 Numbers k such that (k!-7)/7 is prime.

Original entry on oeis.org

7, 9, 20, 23, 46, 54, 57, 71, 85, 387, 396, 606, 1121, 2484, 6786, 9321, 11881, 18372
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Comments

a(19) > 25000. - Robert Price, Nov 05 2016

Crossrefs

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! - 7)/7], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a (*Artur Jasinski*)

Extensions

More terms from Alexis Olson (AlexisOlson(AT)gmail.com), Nov 14 2008
a(13)-a(14) PRPs from Sean A. Irvine, Aug 05 2010
a(15)-a(18) PRP from Robert Price, Nov 05 2016

A139203 Numbers k such that (k!-8)/8 is prime.

Original entry on oeis.org

4, 6, 8, 10, 11, 16, 19, 47, 66, 183, 376, 507, 1081, 1204, 12111, 23181
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Comments

a(17) > 25000. - Robert Price, Oct 08 2016

Crossrefs

Programs

  • Maple
    a:=proc(n) if isprime((1/8)*factorial(n)-1)=true then n else end if end proc: seq(a(n),n=4..550); # Emeric Deutsch, May 07 2008
  • Mathematica
    a = {}; Do[If[PrimeQ[(n! - 8)/8], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a

Extensions

2 more terms from Emeric Deutsch, May 07 2008
More terms from Serge Batalov, Feb 18 2015
a(15)-a(16) from Robert Price, Oct 08 2016

A139204 Numbers k such that (k!-9)/9 is prime.

Original entry on oeis.org

6, 15, 17, 18, 21, 27, 29, 30, 37, 47, 50, 64, 125, 251, 602, 611, 1184, 1468, 5570, 10679, 15798, 21237
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Comments

a(20) > 10000. The PFGW program has been used to certify all the terms up to a(19), using a deterministic test which exploits the factorization of a(n) + 1. - Giovanni Resta, Mar 28 2014
a(23) > 25000. - Robert Price, Mar 29 2017

Crossrefs

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! - 9)/9], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a
  • PARI
    for(n=1,1000,if(floor(n!/9-1)==n!/9-1,if(ispseudoprime(n!/9-1),print(n)))) \\ Derek Orr, Mar 28 2014

Extensions

a(14)-a(16) from Derek Orr, Mar 28 2014
a(17)-a(19) from Giovanni Resta, Mar 28 2014
a(20)-a(22) from Robert Price, Mar 29 2017

A139207 Smallest father factorial prime p of order n = smallest prime of the form (p!-n)/n where p is prime.

Original entry on oeis.org

5, 2, 2947253997913233984847871999999, 29, 23, 19, 719, 4989599, 39520825343999, 11, 11058645491711999, 419, 479001599, 359, 7, 860234568201646565394748723848806399999999
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Comments

For smallest daughter factorial prime p of order n (smallest p such that (p!+n)/n = p!/n + 1 is prime) see A139074.
For smallest son factorial prime p of order n = smallest prime of the form (p!-n)/n where p is prime see A139206.
For more terms see A139206.

Crossrefs

Programs

  • Mathematica
    a = {}; Do[k = 1; While[ ! PrimeQ[(Prime[k]! - n)/n], k++ ]; Print[a]; AppendTo[a, (Prime[k]! - n)/n], {n, 1, 100}]; a
Previous Showing 11-18 of 18 results.