A075410 a(n) is the smallest m such that n!!-m and n!!+m are both primes.

0, 0, 3, 2, 5, 2, 5, 8, 7, 4, 19, 16, 29, 68, 97, 16, 109, 86, 19, 158, 17, 172, 41, 16, 529, 106, 263, 212, 163, 302, 593, 302, 607, 262, 311, 428, 227, 106, 1271, 8, 229, 386, 1489, 32, 47, 1996, 1097, 2566, 41, 632, 1913, 458, 149, 1244, 2837, 362, 3317, 908

Offset

2,3

Comments

For n = 5,7,10,11,22,41,67,76,91,96,163,245,299,341, n!! is an interprime, the average of two consecutive primes, see A075275. See also n^n and n! as average of two primes in A075468 and A075409.

Links

Table of n, a(n) for n=2..59.

Example

a(4) = 3 because 4!! = 8 and 8 -/+ 3 = 5 and 11 are primes with smallest equal distances from 4!!

Mathematica

smbp[n_]:=Module[{m=0, n2=n!!}, While[Total[Boole[PrimeQ[n2+{m, -m}]]] != 2, m++]; m]; Array[smbp, 60, 2] (* Harvey P. Dale, Sep 02 2017 *)

Crossrefs

Cf. A075275, A075468 and A075409.

Sequence in context: A366687 A154421 A057034 * A023513 A069735 A358536

Adjacent sequences: A075407 A075408 A075409 * A075411 A075412 A075413

Keyword

nonn

Author

Zak Seidov, Sep 18 2002

Extensions

More terms from David Wasserman, Jan 17 2005

Status

approved