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

Author

Zak Seidov, Sep 18 2002

Keywords

• nonn

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.

Examples

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

Crossrefs

Cf. A075275, A075468 and A075409.

Programs

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 *)

Extensions

More terms from David Wasserman, Jan 17 2005