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.

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A139063 Numbers k for which (6+k!)/6 is prime.

Original entry on oeis.org

3, 4, 10, 11, 13, 14, 17, 21, 82, 115, 165, 167, 173, 174, 208, 225, 380, 655, 1187, 2000, 2568, 3010, 4542, 8750, 12257, 12601, 24083
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

For primes of the form (6+k!)/6, see A139062.
a(28) > 25000. - Robert Price, Nov 20 2016

Crossrefs

Cf. A082672, A089085, A089130, A117141, A007749, A139056, A139057, A139058, A139059, A139060, A139061, A139061, A139062, A139063, A139064, A139065, A139066, A020458.
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! + 6)/6], AppendTo[a, n]], {n, 1, 500}]; a
  • PARI
    for(k=3,1e3,if(ispseudoprime(k!/6+1),print1(k", "))) \\ Charles R Greathouse IV, Jul 15 2011

Extensions

a(18) and a(19) from Robert Israel, May 19 2014
More terms from Serge Batalov, Feb 18 2015
a(24)-a(27) from Robert Price, Nov 20 2016

A139065 Numbers k for which (7+k!)/7 is prime.

Original entry on oeis.org

11, 15, 16, 25, 35, 59, 64, 68, 82, 121, 149, 238, 584, 912, 3349, 4111, 4324, 15314, 19944, 20658, 22740, 23364
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

For primes of the form (7+k!)/7, see A139064.
a(23) > 25000. - Robert Price, Nov 20 2016

Crossrefs

Cf. A082672, A089085, A089130, A117141, A007749, A139056, A139057, A139058, A139059, A139060, A139061, A139061, A139062, A139063, A139064, A139065, A139066, A020458.
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! + 7)/7], AppendTo[a, n]], {n, 1, 500}]; a
Select[Range[500],PrimeQ[(7+#!)/7]&] (* Harvey P. Dale, Sep 01 2014 *)
  • PARI
    for(k=7,1e3,if(ispseudoprime(k!/7+1),print1(k", "))) \\ Charles R Greathouse IV, Jul 15 2011

Extensions

More terms from Serge Batalov, Feb 18 2015
a(18)-a(22) from Robert Price, Nov 20 2016

A139157 a(n) = (n!+10)/10.

Original entry on oeis.org

13, 73, 505, 4033, 36289, 362881, 3991681, 47900161, 622702081, 8717829121, 130767436801, 2092278988801, 35568742809601, 640237370572801, 12164510040883201, 243290200817664001, 5109094217170944001
Offset: 5

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Links

Crossrefs

Cf. A007749, A020458, A082672, A089085, A089130, A117141, A139056-A139066, A139068, A137390, A139070-A139075, A139148-A139156, A139159, A139160, A139161, A139162.

Programs

  • Mathematica
    Table[(n! + 10)/10, {n, 5, 30}]
  • PARI
    for(n=5, 20, a=(n!+10)/10; print1(a, ", ")) \\ Felix Fröhlich, Jul 07 2014

Extensions

Name corrected by Amiram Eldar, Oct 14 2024

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

A082671 Numbers n such that (n!-2)/2 is a prime.

Original entry on oeis.org

3, 4, 5, 6, 9, 31, 41, 373, 589, 812, 989, 1115, 1488, 1864, 1918, 4412, 4686, 5821, 13830
Offset: 1

Views

Author

Cino Hilliard, May 18 2003

Keywords

Examples

			(4!-2)/2 = 11 is a prime.

Crossrefs

Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199, A139200, A139201, A139202, A139203, A139204, A139205; n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071

Programs

  • Magma
    [n: n in [1..600]| IsPrime((Factorial(n)-2) div 2)]; // Vincenzo Librandi, Feb 18 2015
  • Mathematica
    Select[Range[0, 14000], PrimeQ[(#! - 2) / 2] &] (* Vincenzo Librandi, Feb 18 2015 *)
  • PARI
    xfactpk(n,k=2) = { for(x=2,n, y = (x!-k)/k; if(isprime(y),print1(x", ")) ) }

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
Edited by T. D. Noe, Oct 30 2008

A139148 Smallest positive integer of the form (m!+n)/n.

Original entry on oeis.org

2, 2, 3, 7, 25, 2, 721, 4, 81, 13, 3628801, 3, 479001601, 361, 9, 46, 20922789888001, 41, 6402373705728001, 7, 241, 1814401, 1124000727777607680001, 2, 145153, 239500801, 13441, 181, 304888344611713860501504000001, 5
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Links

Crossrefs

Cf. A002034, A007672, A082672, A089085, A089130, A117141, A007749, A139056-A139066, A020458, A139068, A137390, A139070-A139075, A139148-A139157, A139159, A139160-A139162.

Programs

  • Mathematica
    a = {}; Do[m = 1; While[ ! IntegerQ[m!/n], m++ ]; AppendTo[a, (m! + n)/n], {n, 1, 50}]; a

Formula

a(n) = (n + (A002034(n))!)/n.
a(n) = A007672(n) + 1. - Charles R Greathouse IV, Dec 09 2014

A139160 a(n)=(prime(n)!+2)/2.

Original entry on oeis.org

2, 4, 61, 2521, 19958401, 3113510401, 177843714048001, 60822550204416001, 12926008369442488320001, 4420880996869850977271808000001, 4111419327088961408862781440000001
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Comments

For numbers of the form (p(n)!+1)/1 see A139159
For numbers of the form (p(n)!+2)/2 see A139160
For numbers of the form (p(n)!+3)/3 see A139161
For numbers of the form (p(n)!+4)/4 see A139162
For numbers of the form (p(n)!+5)/5 see A139163
For numbers of the form (p(n)!+6)/6 see A139164
For numbers of the form (p(n)!+7)/7 see A139165
For numbers of the form (p(n)!+8)/8 see A139166
For numbers of the form (p(n)!+9)/9 see A139089
For numbers of the form (p(n)!+10)/10 see A139168
For offsets for above sequences see A139169
For smallest integers of the form (p(m)!+n)/n see A139170

Crossrefs

Cf. A082672, A089085, A089130, A117141, A007749, A139056-A139066, A020458, A139068, A137390, A139070-A139075, A139148-A139157, A139159, A139160-A139166, A139089, A139168-A139170.

Programs

  • Mathematica
    Table[(Prime[n]! + 2)/2, {n, 1, 30}]
  • PARI
    a(n)=prime(n)!/2 + 1 \\ Charles R Greathouse IV, Apr 29 2015

A139199 Numbers k such that (k!-4)/4 is prime.

Original entry on oeis.org

4, 5, 6, 7, 8, 10, 15, 18, 23, 157, 165, 183, 184, 362, 611, 908, 2940, 6875, 9446, 16041
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Comments

Numbers k such that (k!-m)/m is prime:
for m=1 see A002982
for m=2 prime or pseudoprime see A082671
for m=3 see A139056
for m=4 see A139199
for m=5 see A139200
for m=6 see A139201
for m=7 see A139202
for m=8 see A139203
for m=9 see A139204
for m=10 see A139205
a(17) > 2000 - Ray G. Opao, Sep 30 2008
a(21) > 25000 - Robert Price, Sep 25 2016

Crossrefs

Cf. A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.
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], Print[a]; AppendTo[a, n]], {n, 1, 184}]; a (*Artur Jasinski*)
  • PARI
    is(n)=n>3 && isprime(n!/4-1) \\ Charles R Greathouse IV, Apr 29 2015

Extensions

a(15)-a(16) from Ray G. Opao, Sep 30 2008
a(17) from Serge Batalov, Feb 18 2015
a(18)-a(20) from Robert Price, Sep 25 2016

A139205 Numbers k such that (k!-10)/10 is prime.

Original entry on oeis.org

5, 6, 7, 11, 13, 17, 28, 81, 87, 433, 640, 647, 798, 1026, 1216, 1277, 3825, 6684
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Comments

a(19) > 25000. - Robert Price, Dec 23 2016

Crossrefs

Cf. A139189, A139190, A139191, A139192, A139193, A139194, A139195, A139196, A139197, A139198.
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], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a (*Artur Jasinski*)
Select[Range[700],PrimeQ[(#!-10)/10]&] (* Harvey P. Dale, Feb 15 2015 *)

Extensions

One additional term (a(12)) from Harvey P. Dale, Feb 15 2015
More terms from Serge Batalov, Feb 18 2015
a(18) from Robert Price, Dec 23 2016

A151913 Numbers n for which (8+n!)/8 is prime.

Original entry on oeis.org

7, 9, 10, 12, 14, 20, 23, 24, 29, 44, 108, 2049, 3072, 4862, 8807, 15089
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

a(17) > 25000. - Robert Price, Dec 20 2016

Crossrefs

For primes of the form (8+k!!)/8 see A139066.
Cf. A089130, A117141, A139035, A139057, A139059, A139060, A139062, A139064, A139067.
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! + 8)/8], AppendTo[a, n]], {n, 1, 500}]; a
  • PARI
    is(n)=n>6 && isprime((8+n!)/8) \\ Charles R Greathouse IV, Apr 29 2016

Extensions

Definition corrected Feb 24 2010
More terms from Serge Batalov, Feb 18 2015
a(15)-a(16) from Robert Price, Dec 20 2016
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