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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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*)

A139161 a(n)=(prime(n)!+3)/3.

Original entry on oeis.org

3, 41, 1681, 13305601, 2075673601, 118562476032001, 40548366802944001, 8617338912961658880001, 2947253997913233984847872000001, 2740946218059307605908520960000001
Offset: 2

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]! + 3)/3, {n, 2, 30}]

A091415 Numbers n such that n!*2^n - 1 is prime.

Original entry on oeis.org

2, 3, 4, 8, 13, 32, 41, 45, 59, 97, 107, 364, 421, 444, 1164, 1663, 3202, 4335, 4841, 13528, 22159, 38095, 50327, 72853
Offset: 1

Views

Author

Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 02 2004

Keywords

Examples

			a(1)=2 because 2!*2^2 - 1 = 7 is prime
a(2)=3 because 3!*2^3 - 1 = 47 is prime

Links

Crossrefs

A093173 gives the corresponding primes.
Cf. A007749, A117141, A092075.

Programs

  • Mathematica
    For[n=1, n<1000,n++, If[PrimeQ[2^n*n!-1], Print[n]]] (Steinerberger)
  • PARI
    f(n)=n!*2^n -1; for (i=1,363,if(isprime(f(i)),print(i)))

Formula

a(n) = A007749(n+1)/2. - Alexander Adamchuk, Sep 23 2006

Extensions

a(12)-a(14) from Stefan Steinerberger, Feb 05 2006
a(15) from Mohammed Bouayoun (Mohammed.Bouayoun(AT)yahoo.fr), Apr 13 2006
More terms from Alexander Adamchuk, Sep 23 2006
Corrected and extended by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
Terms a(22)..a(24) (using A007749) from Joerg Arndt, Apr 22 2016

A139072 Smallest parameter k such that (n+k!)/n is prime.

Original entry on oeis.org

1, 2, 3, 4, 7, 3, 11, 7, 8, 5, 13, 4, 28, 10, 7, 8, 43, 6, 21, 5, 7, 16, 48, 4, 14, 17, 9, 7, 241, 5, 61, 11, 17, 17, 8, 10, 44, 38, 16, 6, 131, 9, 63, 12, 6, 43, 73, 9, 15, 10, 19, 14, 64, 11, 12, 9, 24, 32, 641, 5, 89, 31, 8, 8, 14, 11, 71, 19, 25, 7, 151, 6, 78, 62, 15, 35, 15, 22, 87
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

a(n) >= A002034(n). - Charles R Greathouse IV, Jul 15 2011
a(878) > 5000. - Jinyuan Wang, Apr 01 2020

Links

Crossrefs

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

Programs

  • Mathematica
    a = {}; Do[k = 1; While[ ! PrimeQ[(k! + n)/n], k++ ]; AppendTo[a, k], {n, 1, 100}]; a
  • PARI
    pr(n)=denominator(n)==1 && ispseudoprime(n)
a(n)=my(k);until(pr(k++!/n+1),);k \\ Charles R Greathouse IV, Jul 15 2011

A139074 a(n) = smallest prime p such that p!/n + 1 is prime, or 0 if no such prime exists.

Original entry on oeis.org

2, 2, 3, 5, 7, 3, 11, 7, 26737, 5, 13, 5
Offset: 1

Views

Author

Artur Jasinski, Apr 08 2008, Apr 21 2008

Keywords

Comments

For the corresponding primes p see A139075.
a(9)>5000, a(13)>5000, a(22)>5000, a(23) = 1579. - Andrew V. Sutherland, Apr 21 2008, Apr 22 2008
a(10)=5, a(11)=13, a(12)=5
a(14)=17, a(15)=7, a(16)=13, a(17)=43, a(18)=7,
a(19)=31, a(20)=5, a(21)=7
a(24)=7, a(25)=47, a(26)=17, a(27)=17, a(28)=7,
a(29)=241, a(30)=5, a(31)=61, a(32)=11, a(33)=17,
a(34)=17, a(35)=29, a(36)=11, a(37)=61, a(38)=103,
a(39)=89, a(40)=7, a(41)=131, a(42)=11, a(43)=71,
a(44)=13, a(45)=7, a(46)=43, a(47)=73, a(48)=67,
a(49)=347, a(50)=31, a(51)=19, a(52)=17, a(53)=347,
a(54)=11, a(55)=13, a(56)=13, a(57)=31, a(58)=73,
a(59)=641, a(60)=5
a(23) = 1579. - Andrew V. Sutherland, Apr 11 2008.
Smallest daughter factorial prime p of order n, i.e. smallest prime of the form (p!+n)/n where p is prime.
For smallest mother factorial prime p of order n see A139075
For smallest father factorial prime p of order n see A139207
For smallest son factorial prime p of order n see A139206
Summary added by Robert Price, Nov 25 2010:
a(1:20)=2,2,3,5,7,3,11,7,26737,5,13,5,>60000,17,7,13,43,7,31,5
a(21:40)=7,>60000,1579,7,47,17,17,7,241,5,61,11,17,17,29,11,61,103,89,7
a(41:60)=131,11,71,13,7,43,73,67,347,31,19,17,347,11,13,13,31,73,641,5
a(61:80)=89,31,13,13,17,11,71,19,131,7,151,7,>10000,641,73,43,17,331,113,11
a(81:100)=13,67,>10000,7,1999,89,31,11,>10000,19,19,31,607,71,61,11,761,23,>10000,83

Examples

			a(1) = 2 because 2 is the first prime and 2!/1 + 1 = 3 is prime
a(2) = 2 because 2 is the first prime and 2!/2 + 1 = 2 is prime
a(3) = 3 because 3!/3 + 1 = 3 is prime

Crossrefs

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

Programs

  • Mathematica
    a = {}; Do[k = 1; While[ ! PrimeQ[(Prime[k]! + n)/n], k++ ]; AppendTo[a, Prime[k]], {n, 1, 8}]; a

Extensions

a(9)-a(12) by Robert Price, Dec 19 2010

A139156 a(n) = (n!+9)/9.

Original entry on oeis.org

81, 561, 4481, 40321, 403201, 4435201, 53222401, 691891201, 9686476801, 145297152001, 2324754432001, 39520825344001, 711374856192001, 13516122267648001, 270322445352960001, 5676771352412160001
Offset: 6

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Links

Crossrefs

Cf. A007749, A020458, A082672, A089085, A089130, A117141, A139056-A139066, A139068, A137390, A139070-A139075, A139148-A139157, A139159, A139160, A139161, A139162.

Programs

  • Mathematica
    Table[(n! + 9)/9, {n, 6, 30}]

Extensions

Name corrected by Amiram Eldar, Oct 14 2024

A093173 Primes of the form (2^n * n!) - 1.

Original entry on oeis.org

7, 47, 383, 10321919, 51011754393599, 1130138339199322632554990773529330319359999999, 73562883979319395645666688474019139929848516028923903999999999, 4208832729023498248022825567687608993477547383960134557368319999999999
Offset: 1

Views

Author

Enoch Haga, Mar 27 2004

Keywords

Comments

Primes resulting from serial multiplication of even numbers, minus 1.
For primes of the form 2^n*n! + 1, trivially a(1)=3, a(2) = 2^259*259! + 1 (593 digits). - Ray Chandler, Mar 27 2004

Examples

			a(1) multiplies the first 2 terms, 2*4-1. a(3) multiplies first 4 terms, a(4) multiplies first 8 terms, a(5) multiplies first 13 terms in 12 multiplications.
a(2)=47, formed by 2*4*6 - 1 = 47.

Links

Crossrefs

Cf. A093154, A093155.
Cf. A117141 (primes of the form n!! - 1).

Programs

  • Mathematica
    lst={};Do[If[PrimeQ[p=(2^n*n!)-1],AppendTo[lst,p]],{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 28 2009 *)
  • PARI
    v=[];for(n=1,404,if(ispseudoprime(t=n!<Charles R Greathouse IV, Feb 14 2011

Formula

Starting with 2, multiply even numbers until the product, minus 1, equals a prime.
a(n) = A117141(n+1). - Alexander Adamchuk, Apr 18 2007

Extensions

More terms from Ray Chandler, Mar 27 2004
a(8) from Robert Price, Mar 13 2015
Previous Showing 21-30 of 49 results. Next

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