|
%I #10 Jul 30 2017 03:45:55
%S 5,7,10,11,22,41,67,76,91,96,163,245,299,341,434,510,535
%N Numbers k such that k!! is an interprime, i.e., the average of two successive primes.
%C The parity of k is opposite to the parity of the differences.
%e 5 is a term because 5!! = 15 is the average of two successive primes, 13 and 17;
%e 163 is a term because 163!! is the average of two successive primes, 163!! -+ 128.
%t 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}]
%Y Cf. A053709. The differences between k!! and its neighboring primes are in A075453.
%K nonn,more
%O 1,1
%A _Zak Seidov_, Sep 12 2002
%E Edited, corrected and extended by _Robert G. Wilson v_, Sep 16 2002
|
