A124082 Numbers k such that prime(k)!/prime(k)# - 1 is prime.

3, 4, 7, 21, 60

Offset: 1

Author

Pierre CAMI, Nov 25 2006

Keywords

• more
• nonn

Comments

No more terms through 1000. - Ryan Propper, Jan 27 2007

No more terms through 2500. - Michael S. Branicky, Oct 02 2024

Examples

			1*2*3*4*5/(2*3*5) - 1 = 3, a prime, so a(1)=3 as 5=prime(3);
1*2*3*4*5*6*7/(2*3*5*7) - 1 = 23, a prime, so a(2)=4 as 7=prime(4);
1*2*3*4*5*6*7*8*9*10*11*12*13*14*15*16*17/(2*3*5*7*11*13*17) - 1 = 696729599, a prime, so a(3)=7 as 17=prime(7).
		

Crossrefs

Cf. A092435 (p!/p#), A124083.

Programs

Mathematica

Primorial[n_] := Times @@ Select[Range[n], PrimeQ]; Do[k = Prime[n]; If[PrimeQ[k!/Primorial[k] - 1], Print[n]], {n, 10^3}] (* Ryan Propper, Jan 27 2007 *)
With[{nn=70},Position[#[[1]]/#[[2]]-1&/@Thread[{Prime[Range[ nn]]!,FoldList[ Times,Prime[Range[nn]]]}],?PrimeQ]//Flatten] (* _Harvey P. Dale, Jul 01 2020 *)

PARI

isok(k) = isprime(prime(k)!/prod(i=1, k, prime(i)) - 1); \\ Michel Marcus, Sep 15 2019