A091421 -id:A091421 - cp's OEIS frontend

A091424 Numbers m such that m#*2^m + 1 is prime, where m# = A002110(m).

1, 3, 4, 6, 10, 30, 31, 98, 156, 230, 432, 490, 1623, 1666, 9324, 9693

Offset: 1

Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 02 2004

1# = 2, 2# = 2*3 = 6, 3# = 2*3*5 = 30.

No more terms < 5000. - L. Joris Perrenet, Mar 17 2020

			a(1) = 1 because 1#*2^1 + 1 = 5 is prime
a(2) = 3 because 3#*2^3 + 1 = 241 is prime

Cf. A002110, A091421.

pp(n)=my(s=1);for(i=1,n,s=s*prime(i));return(s);
f(n)=pp(n)*2^n +1;
for (i=1,500,if(isprime(f(i)),print1(i, ", ")))

a(13)-a(14) from Chai Wah Wu, Dec 23 2019

a(15)-a(16) from Michael S. Branicky, Aug 31 2024

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

Original entry on oeis.org

0, 1, 2, 11, 17, 25, 38, 53, 107, 245, 255, 367, 719, 1077, 2189, 2853, 3236, 3511, 3633, 4531, 4858, 5422, 7787, 8319

Offset: 1

Jason Earls, Jul 15 2005

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)

Cf. A049420, A091421.

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 *)

a(23)-a(24) from Michael S. Branicky, Oct 01 2024

cp's OEIS Frontend

A091424 Numbers m such that m#*2^m + 1 is prime, where m# = A002110(m).

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

Extensions