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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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

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}]

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}]

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

A139092 a(n) = number of distinct prime divisors of (9+prime(n)!)/9.

Original entry on oeis.org

3, 3, 2, 2, 2, 3, 2, 3, 4, 4, 5, 3, 3, 6, 5, 2, 3, 4, 3, 3, 4, 4, 4, 3, 7, 3, 3
Offset: 4

Views

Author

Artur Jasinski, Apr 08 2008

Keywords

Comments

Conjecture: all prime divisors in A139089 are distinct
a(31) >= 4. - Amiram Eldar, Feb 13 2020

Links

Crossrefs

Cf. A082672, A089085, A089130, A117141, A007749, A139056-A139066, A020458, A139068, A137390, A139070-A139075, A136019, A136020, A136026, A136027, A139089-A139092.

Programs

  • Mathematica
    a = {}; Do[w = (Prime[n]! + 9)/9; AppendTo[a, w], {n, 4, 16}]; a
PrimeNu[(9+Prime[Range[4,25]]!)/9] (* Harvey P. Dale, Jul 25 2019 *)

Formula

a(n) = A001221(A139089(n)). - Amiram Eldar, Feb 13 2020

Extensions

More terms from Jon E. Schoenfield, Jul 16 2010
a(23)-a(30) using factordb.com from Amiram Eldar, Feb 13 2020
Previous Showing 21-30 of 49 results. Next

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