A057034 -id:A057034 - cp's OEIS frontend

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

Robert G. Wilson v, Sep 09 2000

nonn

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.

Cf. A006882, A057034.

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 *)

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

A058024 a(n) = A051451(n) - A058023(n).

Original entry on oeis.org

3, 5, 7, 11, 11, 17, 19, 23, 17, 43, 59, 37, 29, 41, 53, 43, 37, 43, 47, 83, 71, 83, 61, 149, 73, 97, 89, 109, 113, 103, 113, 89, 137, 167, 157, 181, 239, 139, 241, 139, 179, 233, 193, 163, 241, 173, 283, 167, 271, 193, 277, 181, 179, 199, 269, 193, 223, 239

Offset: 3

Labos Elemer, Nov 15 2000

nonn

			So far, all terms are primes. The analogy with fortunate numbers (A005235) is clear.

Sean A. Irvine, Table of n, a(n) for n = 3..256

Cf. A000961, A003418, A005235, A051451, A052017, A055211, A057034.

Edited by N. J. A. Sloane, Aug 20 2021

Name corrected by Sean A. Irvine, Jul 18 2022

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

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A058024 a(n) = A051451(n) - A058023(n).

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