cp's OEIS Frontend

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

%I A093154 #18 Sep 08 2022 08:45:13
%S A093154 5,193,23041,92897281,980995276801,23310331287699456001,
%T A093154 31888533201572855808001,13532215908553332190020108288000001,
%U A093154 8829205774994708066835865418197893120000001,945837910352576904120619801361499836578686566400000001
%N A093154 Primes resulting from serial multiplication of even composites, plus 1.
%C A093154 Primes of the form 2^n*(n+1)!+1.
%C A093154 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 A093154 Conjecture that a(13) is the last prime of this form is false:
%C A093154   a(14) = 2^2789*2780!+1 is prime
%C A093154   a(15) = 2^3142*3143!+1 is prime
%C A093154   a(16) = 2^3557*3558!+1 is prime
%C A093154   a(17) = 2^3686*3687!+1 is prime
%C A093154   a(18) = 2^4190*4191!+1 is prime
%C A093154   a(19) = 2^7328*7329!+1 is prime
%C A093154   See A248879. - _Robert Price_, Mar 10 2015
%F A093154 Starting with 4, multiply even composites until the product plus 1 equals a prime.
%e A093154 a(1) = 5 = 2*2!+1
%e A093154 a(2) = 193 = 2^3*4!+1
%e A093154 a(3) = 23041 = 2^5*6!+1
%e A093154 a(4) = 92897281 = 2^8*9!+1
%e A093154 a(5) = 980995276801 = 2^11*12!+1
%e A093154 a(6) = 23310331287699456001 = 2^16*17!+1
%e A093154 a(11) = 2^87*88!+1 is too large to include.
%t A093154 Select[Table[2^n (n + 1)! + 1, {n, 1, 100}], PrimeQ] (* _Vincenzo Librandi_, Mar 10 2015 *)
%o A093154 (Magma) [a: n in [1..40] | IsPrime(a) where a is 2^n*Factorial(n+1)+1]; // _Vincenzo Librandi_, Mar 10 2015
%Y A093154 Cf. A093155, A248879.
%K A093154 easy,nonn
%O A093154 1,1
%A A093154 _Enoch Haga_, Mar 25 2004
%E A093154 Edited and extended by _Ray Chandler_, Mar 27 2004
%E A093154 a(10) from _Robert Price_, Mar 10 2015