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 1-6 of 6 results.

A139068 Primes of the form k!/9 + 1.

Original entry on oeis.org

4481, 611402462201343216650033936533361654773516861440000000001, 234195255375503079690400057633265510581087082006817356924774723468294901747510352675631491470712754833859385753600000000000000000001
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

For numbers k for which (9+k!)/9 is prime see A137390.

Links

Crossrefs

Cf. A020458, A007749, A082672, A089085, A089130, A117141, A137390, A139056, A139057, A139058, A139059, A139060, A139061, A139062, A139063, A139064, A139065, A139066, A137390, A139070, A139071, A139072, A139156.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! + 9)/9], AppendTo[a, (n! + 9)/9]], {n, 1, 150}]; a
Select[Range[100]!/9+1,PrimeQ] (* Harvey P. Dale, Aug 17 2017 *)
  • PARI
    for(n=6,1e4,if(ispseudoprime(t=n!/9+1),print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011

Formula

a(n) = A139156(A137390(n)). - Amiram Eldar, Oct 14 2024

A139070 Primes of the form (10+k!)/10.

Original entry on oeis.org

13, 73, 3991681, 47900161, 130767436801, 2585201673888497664001, 40329146112660563558400001, 1376375309122634504631597958158090240000001, 11962222086548019456196316149565771506438373376000000001
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

For numbers k for which (10+k!)/10 is prime see A139071.

Links

Crossrefs

Cf. A020458, A082672, A089085, A089130, A117141, A007749, A139056, A139057, A139058, A139059, A139060, A139061, A139062, A139063, A139064, A139065, A139066, A139068, A137390, A139071, A139072, A139157.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! + 10)/10], AppendTo[a, (n! + 10)/10]], {n, 1, 50}]; a
Select[(Range[50]!+10)/10,PrimeQ] (* Harvey P. Dale, Sep 18 2013 *)
  • PARI
    for(k=5,1e3,if(ispseudoprime(t=k!/10+1),print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011

Formula

a(n) = A139157(A139071(n)). - Amiram Eldar, Oct 14 2024

A139061 Numbers n for which (4+n!)/4 is prime.

Original entry on oeis.org

4, 5, 6, 13, 21, 25, 32, 40, 61, 97, 147, 324, 325, 348, 369, 1290, 1342, 3167, 6612, 8176, 10990
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

For primes of the form (4+k!)/4, see A139060.
a(22) > 25000. - Robert Price, Jan 10 2017

Crossrefs

Cf. A082672, A089085, A089130, A117141, A007749, A139056, A139057, A139058, A139059, A139060, A139061, A139061, A139062, A139063, A139064, A139065, A139066, A020458, A139068, A137390, A139070, A139071, A139072.
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! + 4)/4], AppendTo[a, n]], {n, 1, 500}]; a
Select[Range[500],PrimeQ[(4+#!)/4]&]  (* Harvey P. Dale, Mar 24 2011 *)
  • PARI
    for(n=4,1e3,if(ispseudoprime(n!/4+1),print1(n", "))) \\ Charles R Greathouse IV, Jul 15 2011

Extensions

More terms from Serge Batalov, Feb 18 2015
a(19) - a(21) from Robert Price, Jan 10 2017

A139071 Numbers k for which (10+k!)/10 is prime.

Original entry on oeis.org

5, 6, 11, 12, 15, 23, 26, 37, 45, 108, 112, 129, 137, 148, 172, 248, 760, 807, 975, 1398, 5231, 8765, 24182
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

Primes of the form (10+k!)/10 see A139070.
a(24) > 25000. - Robert Price, Nov 08 2016

Crossrefs

Cf. A082672, A089085, A089130, A117141, A007749, A139056, A139057, A139058, A139059, A139060, A139061, A139061, A139062, A139063, A139064, A139065, A139066, A020458, A139068, A137390, A139070, A139071, A139072.
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071 (1<=m<=10).

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! + 10)/10], AppendTo[a, n]], {n, 1, 500}]; a
  • PARI
    for(k=5,1e3,if(ispseudoprime(k!/10+1),print1(k", "))) \\ Charles R Greathouse IV, Jul 15 2011

Extensions

More terms from Serge Batalov, Feb 18 2015
a(22)-a(23) from Robert Price, Nov 08 2016

A139073 Smallest prime number of the form (n+k!)/n.

Original entry on oeis.org

2, 2, 3, 7, 1009, 2, 5702401, 631, 4481, 13, 566092801, 3, 23452949585516450807808000001, 259201, 337, 2521, 3553839003727872684550301886383176323956736000000001, 41
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Links

Crossrefs

Cf. A007749, A020458, A082672, A089085, A089130, A117141, A136019, A136020, A136026, A136027, A137390, A139056-A139066, A139068, A139070-A139075.

Programs

  • Mathematica
    a = {}; Do[ k = 1; While[ ! PrimeQ[ (k! + n)/n ], k++ ]; AppendTo[ a, (k! + n)/n ], {n, 1, 100} ]; a [Corrected May 06 2008]
  • PARI
    a(n)=my(k,t);until(denominator(t=k++!/n+1)==1&&ispseudoprime(t),);t \\ Charles R Greathouse IV, Jul 19 2011

Formula

a(n) = (n + A139072(n)!)/n. - Amiram Eldar, Oct 14 2024

A240622 Least number k such that k!/n - 1 is prime.

Original entry on oeis.org

3, 3, 4, 4, 5, 4, 7, 4, 6, 5, 15, 6, 13, 7, 5, 9, 38, 8, 21, 5, 7, 19, 27, 6, 15, 14, 10, 7, 30, 5, 31, 8, 12, 18, 8, 6, 47, 53, 13, 5, 127, 10, 67, 11, 16, 27, 51, 8, 14, 26, 17, 16, 77, 9, 23, 7, 184, 56, 123, 6, 66, 203, 7, 9, 13, 13, 74, 42, 26, 7, 75, 9, 205
Offset: 1

Views

Author

Derek Orr, Apr 09 2014

Keywords

Comments

a(263) > 5000. - Jinyuan Wang, Mar 31 2020

Examples

			1!/1 - 1 = 0 is not prime. 2!/1 - 1 = 1 is not prime. 3!/1 - 1 = 5 is prime. Thus, a(1) = 3.

Links

Crossrefs

Cf. A139072, A139186.

Programs

  • Mathematica
    lnk[n_]:=Module[{k=1},While[!PrimeQ[k!/n-1],k++];k]; Array[lnk,80] (* Harvey P. Dale, Aug 31 2015 *)
  • PARI
    a(n) = {for(k=1, oo, s=k!/n-1; if(floor(s)==s, if(ispseudoprime(s), return(k)))); }
Showing 1-6 of 6 results.

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

Content is available under The OEIS End-User License Agreement.