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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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

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

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

Crossrefs

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

Programs

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

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. 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

A139089 a(n) = prime(n)!/9 + 1.

Original entry on oeis.org

561, 4435201, 691891201, 39520825344001, 13516122267648001, 2872446304320552960001, 982417999304411328282624000001, 913648739353102535302840320000001
Offset: 4

Views

Author

Artur Jasinski, Apr 08 2008

Keywords

Crossrefs

Programs

  • Mathematica
    Table[(Prime[n]! + 9)/9, {n, 4, 30}]
    Prime[Range[4,12]]!/9+1 (* Harvey P. Dale, Aug 22 2020 *)

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.

Crossrefs

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

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

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

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

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.

Crossrefs

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
Previous Showing 11-20 of 49 results. Next