login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A093154 Primes resulting from serial multiplication of even composites, plus 1. 3
5, 193, 23041, 92897281, 980995276801, 23310331287699456001, 31888533201572855808001, 13532215908553332190020108288000001, 8829205774994708066835865418197893120000001, 945837910352576904120619801361499836578686566400000001 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

LINKS

Table of n, a(n) for n=1..10.

FORMULA

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

EXAMPLE

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.

MATHEMATICA

Select[Table[2^n (n + 1)! + 1, {n, 1, 100}], PrimeQ] (* Vincenzo Librandi, Mar 10 2015 *)

PROG

(MAGMA) [a: n in [1..40] | IsPrime(a) where a is 2^n*Factorial(n+1)+1]; // Vincenzo Librandi, Mar 10 2015

CROSSREFS

Cf. A093155, A248879.

Sequence in context: A240639 A198482 A198523 * A194572 A068793 A194573

Adjacent sequences:  A093151 A093152 A093153 * A093155 A093156 A093157

KEYWORD

easy,nonn

AUTHOR

Enoch Haga, Mar 25 2004

EXTENSIONS

Edited and extended by Ray Chandler, Mar 27 2004

a(10) from Robert Price, Mar 10 2015

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 23 17:41 EDT 2021. Contains 346259 sequences. (Running on oeis4.)