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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A139155 a(n) = (n!+8)/8.

Original entry on oeis.org

4, 16, 91, 631, 5041, 45361, 453601, 4989601, 59875201, 778377601, 10897286401, 163459296001, 2615348736001, 44460928512001, 800296713216001, 15205637551104001, 304112751022080001, 6386367771463680001
Offset: 4

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Crossrefs

Programs

  • Mathematica
    Table[(n! + 8)/8, {n, 4, 30}]

Extensions

Name corrected by Amiram Eldar, Oct 14 2024

A139163 a(n) = (prime(n)!+5)/5.

Original entry on oeis.org

25, 1009, 7983361, 1245404161, 71137485619201, 24329020081766401, 5170403347776995328001, 1768352398747940390908723200001, 1644567730835584563545112576000001
Offset: 3

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Crossrefs

Programs

A139169 a(n)=smallest k >= 1 such that n divides prime(k)!.

Original entry on oeis.org

1, 1, 2, 3, 3, 2, 4, 3, 4, 3, 5, 3, 6, 4, 3, 4, 7, 4, 8, 3, 4, 5, 9, 3, 5, 6, 5, 4, 10, 3, 11, 5, 5, 7, 4, 4, 12, 8, 6, 3, 13, 4, 14, 5, 4, 9, 15, 4, 7, 5, 7, 6, 16, 5, 5, 4, 8, 10, 17, 3, 18, 11, 4, 5, 6, 5, 19, 7, 9, 4, 20, 4, 21, 12, 5, 8, 5, 6, 22, 4, 5, 13, 23, 4, 7, 14, 10, 5, 24, 4, 6, 9, 11, 15
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Crossrefs

Programs

  • Maple
    f:= proc(n) local F,m,Q,E,p;
      F:= ifactors(n)[2];
      m:= nops(F);
      Q:= map(t -> t[1],F);
      E:= map(t -> t[2],F);
      p:= max(Q)-1;
      do
        p:= nextprime(p);
        if andmap(i -> add(floor(p/Q[i]^j),j=1..floor(log[Q[i]](p))) >= E[i], [$1..m]) then return p fi;
      od
    end proc:
    f(1):= 2:
    map(numtheory:-pi @ f, [$1..100]); # Robert Israel, Mar 07 2018
  • Mathematica
    a = {}; Do[m = 1; While[ ! IntegerQ[Prime[m]!/n], m++ ]; AppendTo[a, m], {n, 1, 100}]; a
  • PARI
    a(n) = forprime(p=2,, if (!(p! % n), return (primepi(p)))); \\ Michel Marcus, Mar 08 2018

A139171 a(n) = smallest prime number p such that p!/n is an integer.

Original entry on oeis.org

2, 2, 3, 5, 5, 3, 7, 5, 7, 5, 11, 5, 13, 7, 5, 7, 17, 7, 19, 5, 7, 11, 23, 5, 11, 13, 11, 7, 29, 5, 31, 11, 11, 17, 7, 7, 37, 19, 13, 5, 41, 7, 43, 11, 7, 23, 47, 7, 17, 11, 17, 13, 53, 11, 11, 7, 19, 29, 59, 5, 61, 31, 7, 11, 13, 11, 67, 17, 23, 7, 71, 7, 73, 37, 11, 19, 11, 13, 79, 7, 11
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Crossrefs

Prime equivalent of Kempner numbers A002034.
For quotients p!/n see A139170.
For indices of primes in this sequence see A139169.

Programs

  • Maple
    f:= proc(n) local F,m,Q,E,p;
      F:= ifactors(n)[2];
      m:= nops(F);
      Q:= map(t -> t[1],F);
      E:= map(t -> t[2],F);
      p:= max(Q)-1;
      do
        p:= nextprime(p);
        if andmap(i -> add(floor(p/Q[i]^j),j=1..floor(log[Q[i]](p))) >= E[i], [$1..m]) then return p fi;
      od
    end proc:
    f(1):= 2:
    map(f, [$1..100]); # Robert Israel, Mar 07 2018
  • Mathematica
    a = {}; Do[m = 1; While[ ! IntegerQ[Prime[m]!/n], m++ ]; AppendTo[a, Prime[m]], {n, 1, 100}]; a
  • PARI
    a(n) = forprime(p=2,, if (!(p! % n), return (p))); \\ Michel Marcus, Mar 08 2018

A139200 Numbers k such that (k!-5)/5 is prime.

Original entry on oeis.org

5, 11, 12, 16, 36, 41, 42, 47, 127, 136, 356, 829, 1863, 2065, 2702, 4509, 7498
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Comments

a(16) > 3000. - Ray G. Opao, Oct 05 2008
a(18) > 25000. - Robert Price, Nov 20 2016

Crossrefs

Programs

  • Magma
    [n: n in [5..500] | IsPrime((Factorial(n)-5) div 5)]; // Vincenzo Librandi, Nov 21 2016
  • Mathematica
    a = {}; Do[If[PrimeQ[(n! - 5)/5], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a (* Artur Jasinski *)

Extensions

a(13)-a(15) from Ray G. Opao, Oct 05 2008
a(16) from Serge Batalov, Feb 18 2015
a(17) from Robert Price, Nov 20 2016

A139201 Numbers k such that (k!-6)/6 is prime.

Original entry on oeis.org

4, 5, 7, 8, 11, 14, 16, 17, 18, 20, 43, 50, 55, 59, 171, 461, 859, 2830, 3818, 5421, 5593, 10118, 10880, 24350
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Comments

a(25) > 25000. - Robert Price, Dec 15 2016

Crossrefs

Programs

  • Maple
    a:=proc(n) if isprime((1/6)*factorial(n)-1)=true then n else end if end proc: seq(a(n),n=4..500); # Emeric Deutsch, Apr 29 2008
  • Mathematica
    a = {}; Do[If[PrimeQ[(n! - 6)/6], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a (* Artur Jasinski *)

Extensions

2 more terms from Emeric Deutsch, Apr 29 2008
More terms from Serge Batalov, Feb 18 2015
a(22)-a(24) from Robert Price, Dec 15 2016

A139202 Numbers k such that (k!-7)/7 is prime.

Original entry on oeis.org

7, 9, 20, 23, 46, 54, 57, 71, 85, 387, 396, 606, 1121, 2484, 6786, 9321, 11881, 18372
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Comments

a(19) > 25000. - Robert Price, Nov 05 2016

Crossrefs

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! - 7)/7], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a (*Artur Jasinski*)

Extensions

More terms from Alexis Olson (AlexisOlson(AT)gmail.com), Nov 14 2008
a(13)-a(14) PRPs from Sean A. Irvine, Aug 05 2010
a(15)-a(18) PRP from Robert Price, Nov 05 2016

A139203 Numbers k such that (k!-8)/8 is prime.

Original entry on oeis.org

4, 6, 8, 10, 11, 16, 19, 47, 66, 183, 376, 507, 1081, 1204, 12111, 23181
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Comments

a(17) > 25000. - Robert Price, Oct 08 2016

Crossrefs

Programs

  • Maple
    a:=proc(n) if isprime((1/8)*factorial(n)-1)=true then n else end if end proc: seq(a(n),n=4..550); # Emeric Deutsch, May 07 2008
  • Mathematica
    a = {}; Do[If[PrimeQ[(n! - 8)/8], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a

Extensions

2 more terms from Emeric Deutsch, May 07 2008
More terms from Serge Batalov, Feb 18 2015
a(15)-a(16) from Robert Price, Oct 08 2016

A139204 Numbers k such that (k!-9)/9 is prime.

Original entry on oeis.org

6, 15, 17, 18, 21, 27, 29, 30, 37, 47, 50, 64, 125, 251, 602, 611, 1184, 1468, 5570, 10679, 15798, 21237
Offset: 1

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Comments

a(20) > 10000. The PFGW program has been used to certify all the terms up to a(19), using a deterministic test which exploits the factorization of a(n) + 1. - Giovanni Resta, Mar 28 2014
a(23) > 25000. - Robert Price, Mar 29 2017

Crossrefs

Programs

  • Mathematica
    a = {}; Do[If[PrimeQ[(n! - 9)/9], Print[a]; AppendTo[a, n]], {n, 1, 300}]; a
  • PARI
    for(n=1,1000,if(floor(n!/9-1)==n!/9-1,if(ispseudoprime(n!/9-1),print(n)))) \\ Derek Orr, Mar 28 2014

Extensions

a(14)-a(16) from Derek Orr, Mar 28 2014
a(17)-a(19) from Giovanni Resta, Mar 28 2014
a(20)-a(22) from Robert Price, Mar 29 2017

A139164 a(n) = (prime(n)!+6)/6.

Original entry on oeis.org

2, 21, 841, 6652801, 1037836801, 59281238016001, 20274183401472001, 4308669456480829440001, 1473626998956616992423936000001, 1370473109029653802954260480000001
Offset: 2

Views

Author

Artur Jasinski, Apr 11 2008

Keywords

Crossrefs

Programs

  • Mathematica
    Table[(Prime[n]! + 6)/6, {n, 2, 30}]

Extensions

Offset corrected by Georg Fischer, Apr 04 2022
Previous Showing 41-50 of 54 results. Next