A057019 Difference between n!! and the first prime after n!! + 1.

2, 3, 2, 3, 2, 5, 2, 5, 2, 7, 4, 11, 16, 11, 8, 17, 4, 19, 64, 17, 2, 17, 2, 13, 8, 71, 2, 61, 4, 19, 118, 59, 32, 23, 82, 19, 178, 41, 4, 101, 8, 41, 4, 59, 16, 47, 16, 131, 298, 29, 64, 31, 16, 83, 194, 31, 2, 41, 298, 53, 316, 193, 8, 67, 334, 53, 32, 43, 226, 149, 386, 37

Offset: 1

Author

Robert G. Wilson v, Sep 09 2000

Keywords

• nonn

Comments

Analogous to the Fortunate numbers, but unlike them, not all terms here are prime. Many odd-indexed terms are powers of two and all even-indexed terms are prime.

Crossrefs

Cf. A006882, A057034.

Programs

Mathematica

NextPrime[ n_Integer ] := (k=n+1; While[ !PrimeQ[ k ], k++ ]; Return[ k ]); f[ n_Integer ] := (p = n!! + 1; q = NextPrime[ p ]; Return[ q - p + 1 ]); Table[ f[ n ], {n, 1, 75} ]
dfnp[n_]:=Module[{df=n!!},NextPrime[df+1]-df]; Array[dfnp,80] (* Harvey P. Dale, Mar 25 2012 *)

MuPAD

for n from 1 to 72 do f := n!!:a := nextprime(f+2)-f:print(a) end_for; // Zerinvary Lajos, Feb 22 2007