A093154 - OEIS

%I #18 Sep 08 2022 08:45:13

%S 5,193,23041,92897281,980995276801,23310331287699456001,

%T 31888533201572855808001,13532215908553332190020108288000001,

%U 8829205774994708066835865418197893120000001,945837910352576904120619801361499836578686566400000001

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

%C Primes of the form 2^n*(n+1)!+1.

%C 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

%C Conjecture that a(13) is the last prime of this form is false:

%C   a(14) = 2^2789*2780!+1 is prime

%C   a(15) = 2^3142*3143!+1 is prime

%C   a(16) = 2^3557*3558!+1 is prime

%C   a(17) = 2^3686*3687!+1 is prime

%C   a(18) = 2^4190*4191!+1 is prime

%C   a(19) = 2^7328*7329!+1 is prime

%C   See A248879. - _Robert Price_, Mar 10 2015

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

%e a(1) = 5 = 2*2!+1

%e a(2) = 193 = 2^3*4!+1

%e a(3) = 23041 = 2^5*6!+1

%e a(4) = 92897281 = 2^8*9!+1

%e a(5) = 980995276801 = 2^11*12!+1

%e a(6) = 23310331287699456001 = 2^16*17!+1

%e a(11) = 2^87*88!+1 is too large to include.

%t Select[Table[2^n (n + 1)! + 1, {n, 1, 100}], PrimeQ] (* _Vincenzo Librandi_, Mar 10 2015 *)

%o (Magma) [a: n in [1..40] | IsPrime(a) where a is 2^n*Factorial(n+1)+1]; // _Vincenzo Librandi_, Mar 10 2015

%Y Cf. A093155, A248879.

%K easy,nonn

%O 1,1

%A _Enoch Haga_, Mar 25 2004

%E Edited and extended by _Ray Chandler_, Mar 27 2004

%E a(10) from _Robert Price_, Mar 10 2015