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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A139059 Primes of the form (5+k!)/5.

Original entry on oeis.org

1009, 72577, 7983361, 17435658241, 24329020081766401, 5170403347776995328001, 23924444173096038912392632299131543012876746752000000001
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

For numbers k for which (5+k!)/5 is prime see A139058.

Links

Crossrefs

Cf. A082672, A089085, A089130, A117141, A007749, A139056-A139066, A139068, A137390, A139070-A139075, A139152.

Programs

  • Magma
    [ a: n in [1..50] | IsPrime(a) and b mod 5 eq 0 where a is b div 5 where b is Factorial(n)+5 ];
  • Mathematica
    a = {}; Do[If[PrimeQ[(n! + 5)/5], AppendTo[a, (n! + 5)/5]], {n, 1, 50}]; a
Select[(5+Range[50]!)/5,PrimeQ] (* Harvey P. Dale, Dec 04 2020 *)
  • PARI
    for(k=5,1e3,if(ispseudoprime(t=(5+k!)/5),print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011

Formula

a(n) = A139152(A139058(n)). - Amiram Eldar, Oct 14 2024

A076680 Numbers k such that 4*k! + 1 is prime.

Original entry on oeis.org

0, 1, 4, 7, 8, 9, 13, 16, 28, 54, 86, 129, 190, 351, 466, 697, 938, 1510, 2748, 2878, 3396, 4057, 4384, 5534, 7069, 10364
Offset: 1

Views

Author

Phillip L. Poplin (plpoplin(AT)bellsouth.net), Oct 25 2002

Keywords

Comments

a(25) > 6311. - Jinyuan Wang, Feb 06 2020

Examples

			k = 7 is a term because 4*7! + 1 = 20161 is prime.

Links

Crossrefs

Cf. m*n!-1 is a prime: A076133, A076134, A099350, A099351, A180627-A180631.
Cf. m*n!+1 is a prime: A051915, A076679-A076683, A178488, A180626, A126896.
Cf. n!/m-1 is a prime: A002982, A082671, A139056, A139199-A139205.
Cf. n!/m+1 is a prime: A002981, A082672, A089085, A139061, A139058, A139063, A139065, A151913, A137390, A139071.

Programs

  • Mathematica
    Select[Range[5000],PrimeQ[4#!+1]&] (* Harvey P. Dale, Mar 23 2011 *)
  • PARI
    is(k) = ispseudoprime(4*k!+1); \\ Jinyuan Wang, Feb 06 2020

Extensions

Corrected (added missed terms 2748, 2878) by Serge Batalov, Feb 24 2015
a(24) from Jinyuan Wang, Feb 06 2020
a(25)-a(26) from Michael S. Branicky, Jul 04 2024

A139057 Primes of the form (k!-3)/3.

Original entry on oeis.org

7, 239, 159667199, 6974263295999, 2947253997913233984847871999999, 98410933013201380282539536547839999999, 20138421021124611879118377356171332502421503999999999
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

Numbers k for which (k! - 3)/3 is prime see A139056.
a(8) is 180 decimal digits long. See formula for more terms. - Derek Orr, Mar 28 2014

Crossrefs

Cf. A089085, A117141, A007749, A139056.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(-3 + n!)/3], AppendTo[a, (-3 + n!)/3]], {n, 1, 100}]; a
Select[(Range[50]!-3)/3,PrimeQ] (* Harvey P. Dale, Nov 27 2015 *)
  • PARI
    for(n=1,1000,if(floor(n!/3-1)==n!/3-1,if(ispseudoprime(n!/3-1),print(n!/3-1)))) \\ Derek Orr, Mar 28 2014

Formula

a(n) = (A139056(n)!-3)/3 for all n. - Derek Orr, Mar 28 2014

Extensions

Definition corrected by Derek Orr, Mar 28 2014

A139166 a(n) = (prime(n)!+8)/8.

Original entry on oeis.org

16, 631, 4989601, 778377601, 44460928512001, 15205637551104001, 3231502092360622080001, 1105220249217462744317952000001, 1027854831772240352215695360000001
Offset: 3

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

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]! + 8)/8, {n, 3, 30}]

A139168 a(n) = (prime(n)! + 10)/10.

Original entry on oeis.org

13, 505, 3991681, 622702081, 35568742809601, 12164510040883201, 2585201673888497664001, 884176199373970195454361600001, 822283865417792281772556288000001
Offset: 3

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

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]! + 10)/10, {n, 3, 30}]

A139060 Primes of the form (4+k!)/4.

Original entry on oeis.org

7, 31, 181, 1556755201, 12772735542927360001, 3877802510832746496000001, 65782709233423382541804503040000001, 203978820811974433586402817399028973568000000001
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

For numbers k for which (4+k!)/4 is prime see A139061.

Links

Crossrefs

Cf. A007749, A020458, A082672, A089085, A089130, A117141, A139056, A139057, A139058, A139059, A139061, A139062, A139063, A139064, A139065, A139066, A139151.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! + 4)/4], AppendTo[a, (n! + 4)/4]], {n, 1, 50}]; a
Select[(4+Range[100]!)/4,PrimeQ] (* Harvey P. Dale, Oct 05 2016 *)
  • PARI
    for(k=4,1e3,if(ispseudoprime(t=k!/4+1),print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011

Formula

a(n) = A139151(A139061(n)). - Amiram Eldar, Oct 13 2024

A139062 Primes of the form (6+k!)/6.

Original entry on oeis.org

2, 5, 604801, 6652801, 1037836801, 14529715201, 59281238016001, 8515157028618240001
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

For numbers k for which (6+k!)/6 is prime see A139063.

Links

Crossrefs

Cf. A020458, A082672, A089085, A089130, A117141, A007749, A139056, A139057, A139058, A139059, A139060, A139061, A139063, A139064, A139065, A139066, A139153.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! + 6)/6], AppendTo[a, (n! + 6)/6]], {n, 1, 50}]; a
  • PARI
    for(k=3,1e3,if(ispseudoprime(t=k!/6+1),print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011

Formula

a(n) = A139153(A139063(n)). - Amiram Eldar, Oct 14 2024

A139064 Primes of the form (7+k!)/7.

Original entry on oeis.org

5702401, 186810624001, 2988969984001, 2215887149047283712000001, 1476163995198020704238093048217600000001, 19811874077955690819705574245769915192271839538955347505831613562880000000000001
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

For numbers k for which (7+k!)/7 is prime see A139065.

Links

Crossrefs

Cf. A020458, A082672, A089085, A089130, A117141, A007749, A139056, A139057, A139058, A139059, A139060, A139061, A139062, A139063, A139065, A139066, A139154.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! + 7)/7], AppendTo[a, (n! + 7)/7]], {n, 1, 50}]; a
  • PARI
    for(k=7,1e3,if(ispseudoprime(t=k!/7+1),print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011

Formula

a(n) = A139154(A139065(n)). - Amiram Eldar, Oct 14 2024

A139162 a(n)=(prime(n)!+4)/4.

Original entry on oeis.org

31, 1261, 9979201, 1556755201, 88921857024001, 30411275102208001, 6463004184721244160001, 2210440498434925488635904000001, 2055709663544480704431390720000001
Offset: 3

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

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]! + 4)/4, {n, 3, 30}]

A139170 a(n) = A136156(n) + 1.

Original entry on oeis.org

3, 2, 3, 31, 25, 2, 721, 16, 561, 13, 3628801, 11, 479001601, 361, 9, 316, 20922789888001, 281, 6402373705728001, 7, 241, 1814401, 1124000727777607680001, 6, 1596673, 239500801, 1478401, 181
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Crossrefs

Cf. A136156.
Cf. A082672, A089085, A089130, A117141, A007749, A139056-A139066, A020458, A139068, A137390, A139070-A139075, A139148-A139157, A139159, A139160-A139166, A139089, A139168-A139170.

Programs

  • Mathematica
    a = {}; Do[m = 1; While[ ! IntegerQ[(n + Prime[m]!)/n], m++ ]; AppendTo[a, (n + Prime[m]!)/n], {n, 1, 100}]; a (*Artur Jasinski*)
Previous Showing 21-30 of 54 results. Next

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

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