A082434 Let q_n be least prime > x_n := 1 + 2*n!; sequence gives a(n) = q_n-x_n+1.

3, 3, 5, 5, 11, 7, 11, 11, 29, 29, 13, 71, 29, 19, 19, 37, 23, 23, 41, 29, 53, 53, 89, 29, 41, 41, 59, 227, 79, 41, 101, 73, 61, 41, 37, 59, 67, 127, 67, 223, 71, 43, 53, 71, 71, 113, 239, 71, 313, 157

Offset: 1

Author

Maciej Ulas (maciejulas(AT)poczta.onet.pl), Apr 25 2003

Keywords

• hard
• nonn

Examples

			a(4) = 5 because 2*4!+1=49, the next prime is 51 and the difference between 53 and 48 is 13.
		

Programs

Mathematica

Do[If[PrimeQ[NextPrime[2*n!+1]-2*n! ], Print[n]], {n, 100}]
f[x_]:=Module[{n=2x!},NextPrime[n+1]-n]
f/@Range[60]  (* Harvey P. Dale, Feb 14 2011 *)

PARI

vector(100,n,nextprime(2*n!+2)-2*n!) \\ Charles R Greathouse IV, Feb 14 2011

Formula

a(n)=nextprime(2*n!+1)-2*n!, where nextprime is A151800.