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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..17.

Example

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.

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}]

Crossrefs

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

Sequence in context: A241265 A189290 A129415 * A245270 A319267 A123122

Adjacent sequences: A075272 A075273 A075274 * A075276 A075277 A075278

Keyword

nonn,more

Author

Zak Seidov, Sep 12 2002

Extensions

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

Status

approved