A057034 Difference between n!! and the first prime before n!! - 1.

3, 2, 5, 2, 5, 4, 7, 4, 7, 4, 23, 2, 19, 2, 97, 2, 19, 64, 17, 62, 19, 4, 17, 58, 23, 64, 157, 122, 47, 106, 47, 4, 29, 146, 31, 64, 29, 8, 71, 8, 43, 32, 31, 128, 67, 122, 41, 2, 37, 146, 137, 122, 191, 142, 59, 128, 71, 284, 109, 274, 101, 218, 97, 32, 83, 158, 53, 166

Offset: 4

Author

Robert G. Wilson v, Sep 09 2000

Keywords

• nonn

Comments

Analogous to the lesser Fortunate numbers but unlike them, all entries are not prime. Must odd entries are powers of two and all even entries are primes.

Crossrefs

Cf. A006882, A057019.

Programs

Mathematica

PrevPrime[ n_Integer ] := (k=n-1; While[ !PrimeQ[ k ], k-- ]; Return[ k ]); f[ n_Integer ] := (p = n!! - 1; q = PrevPrime[ p ]; Return[ p - q + 1 ]); Table[ f[ n ], {n, 4, 75} ]