A108894 Numbers n such that (n!/n#) * 2^n + 1 is prime, where n# = primorial numbers (A034386).

0, 1, 2, 11, 17, 25, 38, 53, 107, 245, 255, 367, 719, 1077, 2189, 2853, 3236, 3511, 3633, 4531, 4858, 5422

Offset

1,3

Comments

n!/n# is known as n compositorial. All values have been proved prime. No more terms up to 6100. Primality proof for the largest, which has 17219 digits: PFGW Version 1.2.0 for Windows [FFT v23.8] Primality testing (5422!/5422#)*(2^5422)+1 [N-1, Brillhart-Lehmer-Selfridge] Running N-1 test using base 2719 Calling Brillhart-Lehmer-Selfridge with factored part 36.34% (5422!/5422#)*(2^5422)+1 is prime! (66.5095s+0.0129s)

Links

Table of n, a(n) for n=1..22.

Mathematica

f[n_] := n!/Fold[Times, 1, Prime[ Range[ PrimePi[ n]]]]*2^n + 1; Do[ If[ PrimeQ[ f[n]], Print[n]], {n, 0, 1100}] (* Robert G. Wilson v, Jul 18 2005 *)

Crossrefs

Cf. A049420, A091421.

Sequence in context: A282509 A225590 A060427 * A233445 A066794 A087379

Adjacent sequences: A108891 A108892 A108893 * A108895 A108896 A108897

Keyword

more,nonn

Author

Jason Earls, Jul 15 2005

Status

approved