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.

Showing 1-10 of 61 results. Next

A139056 Numbers k for which (k!-3)/3 is prime.

Original entry on oeis.org

4, 6, 12, 16, 29, 34, 43, 111, 137, 181, 528, 2685, 39477, 43697
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

Corresponding primes (k!-3)/3 are in A139057.
a(13) > 10000. The PFGW program has been used to certify all the terms up to a(12), using a deterministic test which exploits the factorization of a(n) + 1. - Giovanni Resta, Mar 28 2014
98166 is a member of the sequence but its index is not yet determined. The interval where sieving and tests were not run is [60000,90000]. - Serge Batalov, Feb 24 2015

Links

Crossrefs

Cf. A007749, A117141.
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.
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.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(-3 + n!)/3], AppendTo[a, n]], {n, 1, 1000}]; a
  • PARI
    for(n=1,1000,if(floor(n!/3-1)==n!/3-1,if(ispseudoprime(n!/3-1),print(n)))) \\ Derek Orr, Mar 28 2014

Extensions

Definition corrected by Derek Orr, Mar 28 2014
a(8)-a(11) from Derek Orr, Mar 28 2014
a(12) from Giovanni Resta, Mar 28 2014
a(13)-a(14) from Serge Batalov, Feb 24 2015

A123910 Numbers k such that k!!-4 is prime.

Original entry on oeis.org

5, 7, 9, 11, 13, 15, 19, 25, 35, 79, 81, 105, 171, 243, 271, 295, 355, 523, 591, 1211, 3073, 11157, 12887, 19825
Offset: 1

Views

Author

Alexander Adamchuk, Oct 28 2006

Keywords

Comments

Corresponding primes of the form k!!-4 = a(n)!!-4 are {11, 101, 941, 10391, 135131, 2027021, 654729071, 7905853580621, 221643095476699771871, ...}.
a(25) > 50000. - Robert Price, May 08 2015

Links

Crossrefs

Cf. A007749, A094144.

Programs

  • Mathematica
    Do[f=n!!-4;If[PrimeQ[f],Print[{n,f}]],{n,1,355}]

Extensions

More terms from Farideh Firoozbakht, Nov 19 2006
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
a(23)-a(24) from Robert Price, May 08 2015

A117141 Primes of the form n!! - 1.

Original entry on oeis.org

2, 7, 47, 383, 10321919, 51011754393599, 1130138339199322632554990773529330319359999999, 73562883979319395645666688474019139929848516028923903999999999, 4208832729023498248022825567687608993477547383960134557368319999999999
Offset: 1

Views

Author

Paolo P. Lava and Giorgio Balzarotti, Apr 21 2006

Keywords

Examples

			6!! - 1 = 6*4*2 - 1 = 48 - 1 = 47, which is prime.
8!! - 1 = 8*6*4*2 - 1 = 384 - 1 = 383, which is prime.

References

  • G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 158.

Links

Crossrefs

Cf. A002981, A002982, A006882, A007749, A088332.
Cf. A093173 = primes of the form (2^n * n!) - 1.

Programs

  • Maple
    SFACT:= proc(n) local i,j,k; for k from 1 by 1 to n do i:=k; j:=k-2; while j >0 do i:=i*j; j:=j-2; od: if isprime(i-1) then print(i-1); fi; od: end: SFACT(100);
  • Mathematica
    lst={};Do[p=n!!-1;If[PrimeQ[p],AppendTo[lst,p]],{n,0,5!,1}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 27 2009 *)
Select[Table[n!!-1,{n,1,100}],PrimeQ] (* Vincenzo Librandi, Dec 07 2011 *)
  • PARI
    print1(2);for(n=1, 1e3, if(ispseudoprime(t=n!<Charles R Greathouse IV, Jun 16 2011

Formula

a(n) = A093173(n-1) for n > 1. - Alexander Adamchuk, Apr 18 2007
a(n) = A006882(A007749(n)) - 1. - Elmo R. Oliveira, Feb 22 2025

A139066 Primes of the form (8+k!)/8.

Original entry on oeis.org

631, 45361, 453601, 59875201, 10897286401, 304112751022080001, 3231502092360622080001, 77556050216654929920001, 1105220249217462744317952000001, 332283946848556096005453226376826986289954816000000001
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

For numbers k for which (8+k!)/8 is prime see A151913.
The next term (a(11)) has 174 digits. - Harvey P. Dale, May 10 2016

Links

Crossrefs

Cf. A020458, A082672, A089085, A089130, A117141, A007749, A139056, A139057, A139058, A139059, A139060, A139061, A139062, A139063, A139064, A139065, A139155, A151913.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! + 8)/8], AppendTo[a, (n! + 8)/8]], {n, 1, 50}]; a
Select[(8+Range[50]!)/8,PrimeQ] (* Harvey P. Dale, May 10 2016 *)
  • PARI
    for(k=4,1e3,if(ispseudoprime(t=k!/8+1),print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011

Formula

a(n) = A139155(A151913(n)). - Amiram Eldar, Oct 14 2024

Extensions

Corrected link to sequence of indexes. - Serge Batalov, Feb 17 2015
a(10) from Harvey P. Dale, May 10 2016

A139068 Primes of the form k!/9 + 1.

Original entry on oeis.org

4481, 611402462201343216650033936533361654773516861440000000001, 234195255375503079690400057633265510581087082006817356924774723468294901747510352675631491470712754833859385753600000000000000000001
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

For numbers k for which (9+k!)/9 is prime see A137390.

Links

Crossrefs

Cf. A020458, A007749, A082672, A089085, A089130, A117141, A137390, A139056, A139057, A139058, A139059, A139060, A139061, A139062, A139063, A139064, A139065, A139066, A137390, A139070, A139071, A139072, A139156.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! + 9)/9], AppendTo[a, (n! + 9)/9]], {n, 1, 150}]; a
Select[Range[100]!/9+1,PrimeQ] (* Harvey P. Dale, Aug 17 2017 *)
  • PARI
    for(n=6,1e4,if(ispseudoprime(t=n!/9+1),print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011

Formula

a(n) = A139156(A137390(n)). - Amiram Eldar, Oct 14 2024

A139070 Primes of the form (10+k!)/10.

Original entry on oeis.org

13, 73, 3991681, 47900161, 130767436801, 2585201673888497664001, 40329146112660563558400001, 1376375309122634504631597958158090240000001, 11962222086548019456196316149565771506438373376000000001
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

For numbers k for which (10+k!)/10 is prime see A139071.

Links

Crossrefs

Cf. A020458, A082672, A089085, A089130, A117141, A007749, A139056, A139057, A139058, A139059, A139060, A139061, A139062, A139063, A139064, A139065, A139066, A139068, A137390, A139071, A139072, A139157.

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! + 10)/10], AppendTo[a, (n! + 10)/10]], {n, 1, 50}]; a
Select[(Range[50]!+10)/10,PrimeQ] (* Harvey P. Dale, Sep 18 2013 *)
  • PARI
    for(k=5,1e3,if(ispseudoprime(t=k!/10+1),print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011

Formula

a(n) = A139157(A139071(n)). - Amiram Eldar, Oct 14 2024

A139075 Primes p arising in A139074.

Original entry on oeis.org

3, 2, 3, 31, 1009, 2, 5702401, 631
Offset: 1

Views

Author

Artur Jasinski, Apr 08 2008, Apr 21 2008

Keywords

Comments

a(23) = (23+1579!)/23. - Andrew V. Sutherland, Apr 11 2008.
Smallest mother factorial prime p of order n, i.e. smallest prime of the form (p!+n)/n where p is prime.
For smallest daughter factorial prime p of order n see A139074.
For smallest father factorial prime p of order n see A139207.
For smallest son factorial prime p of order n see A139206.
a(9)=26737!/9+1 is a 106758 digit (probable) prime. Easily calculated but too large to enter here a(10)=13, a(11)=566092801, a(12)=11. [Robert Price, Jan 19 2011]

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[(Prime[k]! + n)/n]], {n, 1, 8}]; a

A080778 Double factorial primes; values k for which k!! + 1 is prime.

Original entry on oeis.org

0, 1, 2, 518, 33416, 37310, 52608, 123998, 220502
Offset: 1

Views

Author

Steven Harvey, Mar 11 2003

Keywords

Comments

Numbers k such that A006882(k) + 1 is prime.
a(1) and a(2) correspond to the same prime, 1+1. For n >= 3, a(n) is even (because (2j+1)!! + 1 is even), and then a(n)/2 equals A256594(n-1). - Jeppe Stig Nielsen, Apr 01 2023

Examples

			518 is included because 518*516*514*...*4*2 + 1 is prime. - _Jeppe Stig Nielsen_, Apr 01 2023

Links

Crossrefs

Cf. A006882, A007749, A256594.

Extensions

a(7) from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 03 2008
a(8) from Sou Fukui, Jun 05 2015
a(9) from Sou Fukui, Jan 17 2017

A139061 Numbers n for which (4+n!)/4 is prime.

Original entry on oeis.org

4, 5, 6, 13, 21, 25, 32, 40, 61, 97, 147, 324, 325, 348, 369, 1290, 1342, 3167, 6612, 8176, 10990
Offset: 1

Views

Author

Artur Jasinski, Apr 07 2008

Keywords

Comments

For primes of the form (4+k!)/4, see A139060.
a(22) > 25000. - Robert Price, Jan 10 2017

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! + 4)/4], AppendTo[a, n]], {n, 1, 500}]; a
Select[Range[500],PrimeQ[(4+#!)/4]&]  (* Harvey P. Dale, Mar 24 2011 *)
  • PARI
    for(n=4,1e3,if(ispseudoprime(n!/4+1),print1(n", "))) \\ Charles R Greathouse IV, Jul 15 2011

Extensions

More terms from Serge Batalov, Feb 18 2015
a(19) - a(21) from Robert Price, Jan 10 2017

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
Showing 1-10 of 61 results. Next

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