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

3, 4, 7, 21, 60

Offset

1,1

Comments

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

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

Links

Table of n, a(n) for n=1..5.

Example

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).

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 *)

Prog

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

Crossrefs

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

Sequence in context: A241660 A338452 A030724 * A056655 A341810 A338511

Adjacent sequences: A124079 A124080 A124081 * A124083 A124084 A124085

Keyword

more,nonn

Author

Pierre CAMI, Nov 25 2006

Status

approved