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 1-3 of 3 results.

A093173 Primes of the form (2^n * n!) - 1.

Original entry on oeis.org

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

Views

Author

Enoch Haga, Mar 27 2004

Keywords

Comments

Primes resulting from serial multiplication of even numbers, minus 1.
For primes of the form 2^n*n! + 1, trivially a(1)=3, a(2) = 2^259*259! + 1 (593 digits). - Ray Chandler, Mar 27 2004

Examples

			a(1) multiplies the first 2 terms, 2*4-1. a(3) multiplies first 4 terms, a(4) multiplies first 8 terms, a(5) multiplies first 13 terms in 12 multiplications.
a(2)=47, formed by 2*4*6 - 1 = 47.

Links

Crossrefs

Cf. A093154, A093155.
Cf. A117141 (primes of the form n!! - 1).

Programs

  • Mathematica
    lst={};Do[If[PrimeQ[p=(2^n*n!)-1],AppendTo[lst,p]],{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 28 2009 *)
  • PARI
    v=[];for(n=1,404,if(ispseudoprime(t=n!<Charles R Greathouse IV, Feb 14 2011

Formula

Starting with 2, multiply even numbers until the product, minus 1, equals a prime.
a(n) = A117141(n+1). - Alexander Adamchuk, Apr 18 2007

Extensions

More terms from Ray Chandler, Mar 27 2004
a(8) from Robert Price, Mar 13 2015

A093155 Primes resulting from serial multiplication of even composites, minus 1.

Original entry on oeis.org

3, 23, 191, 23039, 322559, 5160959, 40874803199, 25505877196799
Offset: 1

Views

Author

Enoch Haga, Mar 25 2004

Keywords

Comments

Primes of the form 2^n*(n+1)! - 1.
a(9) has 193 digits, a(10) has 230 digits. - Vincenzo Librandi, Mar 08 2015

Examples

			a(1) = 3 = 2*2! - 1.
a(2) = 23 = 2^2*3! - 1.
a(3) = 191 = 2^3*4! - 1.
a(4) = 23039 = 2^5*6! - 1.
a(5) = 322559 = 2^6*7! - 1.
a(6) = 5160959 = 2^7*8! - 1.
a(7) = 40874803199 = 2^10*11! - 1.
a(8) = 25505877196799 = 2^12*13! - 1.
a(9) = 2^101*102! - 1 is too large to include.
a(10) = 2^117*118! - 1; a(11) = 2^227*228! - 1. - _Jorge Coveiro_, Dec 24 2004

Crossrefs

Cf. A093154, A101323.

Programs

  • Magma
    [a: n in [0..100] | IsPrime(a) where a is 2^n*Factorial(n+1)-1]; // Vincenzo Librandi, Mar 08 2015
  • Mathematica
    Select[Table[2^n (n + 1)! - 1, {n, 0, 300}], PrimeQ] (* Vincenzo Librandi, Mar 08 2015 *)
  • PARI
    for(x=1,500,if(isprime(2^x*(x+1)!-1),print1(x, ", "))) \\ Jorge Coveiro, Dec 24 2004

Formula

Starting with 4, multiply even composites until the product minus 1 equals a prime.

Extensions

Edited by Ray Chandler, Mar 27 2004
The next term is too large to include.

A248879 Numbers k >= 0 such that 2^k*(k+1)!+1 is prime.

Original entry on oeis.org

0, 1, 3, 5, 8, 11, 16, 18, 25, 30, 36, 87, 118, 142, 2789, 3142, 3557, 3686, 4190, 7328
Offset: 1

Views

Author

Robert Price, Mar 05 2015

Keywords

Comments

a(21) > 10^4.

Examples

			a(3) = 2^3*(3+1)!+1 = 193 which is prime.

Crossrefs

Cf. A093154.

Programs

  • Mathematica
    Select[Range[0,10000], PrimeQ[2^#*(#+1)!+1] &]
  • PARI
    for(n=0,10^3,if(ispseudoprime((n+1)!*2^n+1),print1(n,", "))) \\ Derek Orr, Mar 06 2015
Showing 1-3 of 3 results.

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

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