A075275 Numbers k such that k!! is an interprime, i.e., the average of two successive primes.

5, 7, 10, 11, 22, 41, 67, 76, 91, 96, 163, 245, 299, 341, 434, 510, 535, 800, 935, 1401, 1403, 1747

Offset: 1

Author

Zak Seidov, Sep 12 2002

Keywords

• nonn
• more

Comments

The parity of k is opposite to the parity of the differences.

a(23) > 3000. - Michael S. Branicky, Jan 20 2025

Examples

			5 is a term because 5!! = 15 is the average of two successive primes, 13 and 17;
163 is a term because 163!! is the average of two successive primes, 163!! -+ 128.
		

Crossrefs

Cf. A053709. The differences between k!! and its neighboring primes are in A075453.

Programs

Mathematica

PrevPrim[n_] := Block[{k = n - 1}, While[ !PrimeQ[k], k-- ]; k]; NextPrim[n_] := Block[{k = n + 1}, While[ !PrimeQ[k], k++ ]; k] Do[ a = n!!; If[ 2a == PrevPrim[a] + NextPrim[a], Print[n]], {n, 3, 762}]

Extensions

Edited, corrected and extended by Robert G. Wilson v, Sep 16 2002

a(18)-a(22) from Michael S. Branicky, Jan 19 2025