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A075275
Numbers k such that k!! is an interprime, i.e., the average of two successive primes.
3
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.
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
KEYWORD
nonn,more
AUTHOR
Zak Seidov, Sep 12 2002
EXTENSIONS
Edited, corrected and extended by Robert G. Wilson v, Sep 16 2002
STATUS
approved