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

A093154 Primes resulting from serial multiplication of even composites, plus 1.

Original entry on oeis.org

5, 193, 23041, 92897281, 980995276801, 23310331287699456001, 31888533201572855808001, 13532215908553332190020108288000001, 8829205774994708066835865418197893120000001, 945837910352576904120619801361499836578686566400000001
Offset: 1

Views

Author

Enoch Haga, Mar 25 2004

Keywords

Comments

Primes of the form 2^n*(n+1)!+1.
a(12) = 2^118*119!+1, a(13) = 2^142*143!+1. I conjecture that a(13) is the last prime number of this form. - Jorge Coveiro, Apr 01 2004
Conjecture that a(13) is the last prime of this form is false:
a(14) = 2^2789*2780!+1 is prime
a(15) = 2^3142*3143!+1 is prime
a(16) = 2^3557*3558!+1 is prime
a(17) = 2^3686*3687!+1 is prime
a(18) = 2^4190*4191!+1 is prime
a(19) = 2^7328*7329!+1 is prime
See A248879. - Robert Price, Mar 10 2015

Examples

			a(1) = 5 = 2*2!+1
a(2) = 193 = 2^3*4!+1
a(3) = 23041 = 2^5*6!+1
a(4) = 92897281 = 2^8*9!+1
a(5) = 980995276801 = 2^11*12!+1
a(6) = 23310331287699456001 = 2^16*17!+1
a(11) = 2^87*88!+1 is too large to include.

Crossrefs

Cf. A093155, A248879.

Programs

  • Magma
    [a: n in [1..40] | IsPrime(a) where a is 2^n*Factorial(n+1)+1]; // Vincenzo Librandi, Mar 10 2015
  • Mathematica
    Select[Table[2^n (n + 1)! + 1, {n, 1, 100}], PrimeQ] (* Vincenzo Librandi, Mar 10 2015 *)

Formula

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

Extensions

Edited and extended by Ray Chandler, Mar 27 2004
a(10) from Robert Price, Mar 10 2015

A101323 Numbers n such that 2^n*(n+1)!-1 is prime.

Original entry on oeis.org

1, 2, 3, 5, 6, 7, 10, 12, 101, 117, 227, 884, 1323, 2167, 3483, 6274, 7887
Offset: 1

Views

Author

Jorge Coveiro, Dec 24 2004

Keywords

Comments

a(18) > 10^4.- Robert Price, Mar 08 2015

Crossrefs

Cf. A093155.

Programs

Extensions

a(12) from Harvey P. Dale, Nov 23 2014
a(13)-a(17) from Robert Price, Mar 08 2015
Showing 1-3 of 3 results.

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