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A093155 Primes resulting from serial multiplication of even composites, minus 1. 3
3, 23, 191, 23039, 322559, 5160959, 40874803199, 25505877196799 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

LINKS

Table of n, a(n) for n=1..8.

FORMULA

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

EXAMPLE

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

MATHEMATICA

Select[Table[2^n (n + 1)! - 1, {n, 0, 300}], PrimeQ] (* Vincenzo Librandi, Mar 08 2015 *)

PROG

(PARI) for(x=1, 500, if(isprime(2^x*(x+1)!-1), print1(x, ", "))) \\ Jorge Coveiro, Dec 24 2004

(MAGMA) [a: n in [0..100] | IsPrime(a) where a is 2^n*Factorial(n+1)-1]; // Vincenzo Librandi, Mar 08 2015

CROSSREFS

Cf. A093154, A101323.

Sequence in context: A074579 A060880 A331718 * A241886 A096649 A235131

Adjacent sequences:  A093152 A093153 A093154 * A093156 A093157 A093158

KEYWORD

easy,nonn

AUTHOR

Enoch Haga, Mar 25 2004

EXTENSIONS

Edited by Ray Chandler, Mar 27 2004

The next term is too large to include.

STATUS

approved

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Last modified August 2 20:38 EDT 2021. Contains 346428 sequences. (Running on oeis4.)