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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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*)

A156167 Numbers n such that n![7]-1 is prime (where n![7] = A114799(n) = septuple factorial).

Original entry on oeis.org

3, 4, 6, 8, 9, 10, 11, 12, 14, 17, 20, 24, 30, 31, 32, 46, 52, 54, 59, 98, 104, 143, 145, 160, 174, 198, 199, 202, 212, 215, 254, 371, 382, 452, 674, 739, 959, 1249, 1657, 2291, 2553, 2650, 3562, 3727, 3853, 4389, 4604, 5449, 5659, 6026, 6878, 7900, 9564, 10150, 12444, 13321, 22642, 24014, 26598, 27430, 31386, 40707, 43328, 45811
Offset: 1

Views

Author

M. F. Hasler, Feb 10 2009

Keywords

Comments

a(65) > 50000. - Robert Price, Sep 09 2012

Links

Crossrefs

cf. A156165, A051592, A085149, A085147, A084438, A007749, A002982.

Programs

  • Mathematica
    MultiFactorial[n_, k_] := If[n < 1, 1, n*MultiFactorial[n - k, k]];
Select[Range[0, 1000], PrimeQ[MultiFactorial[#, 7] - 1] & ] (* Robert Price, Apr 19 2019 *)
  • PARI
    mf(n,k=7)=prod(i=0,(n-2)\k,n-i*k)
for( n=1,9999, ispseudoprime(mf(n)-1) & print1(n","))

Extensions

a(43)-a(64) from Robert Price, Sep 09 2012

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

A258616 Numbers n such that n!!-16 is prime.

Original entry on oeis.org

7, 9, 13, 17, 25, 185, 197, 261, 407, 593, 1535, 2129, 2139, 2581, 4133, 4665, 15787, 25337, 27449
Offset: 1

Views

Author

Robert Price, Jun 05 2015

Keywords

Comments

Corresponding primes are 89, 929, 135119, 34459409, ... .
a(20) > 50000.

Links

Crossrefs

Cf. A006882, A007749, A094144, A123910.

Programs

  • Mathematica
    Select[Range[4,1000],PrimeQ[#!!-16]&] (* Robert Price, Jun 05 2015 *)
Do[f=n!! - 16; If[PrimeQ[f], Print[{n, f}]], {n, 4, 600}] (* Vincenzo Librandi, Jun 06 2015 *) (see comment)
Previous Showing 21-30 of 61 results. Next

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

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