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A218123 Denominators of terms of the sequence {c(n)} defined in A218121.

%I A218123 #20 Dec 05 2012 03:17:53
%S A218123 1,2,2,2,2,3,3,3,5,5,5,7,7,7,7,7,7,11,11,11,11,13,13,13,13,13,13,17,
%T A218123 17,17,17,17,17,19,19,19,19,19,19,19,23,23,23,23,23,23,23,23,29,29,29,
%U A218123 29,31,31,31,31,31,31,31,31,31,37,37,37,37,37,37,41,41,41,41,43,43,43,43,43,43,43,47,47
%N A218123 Denominators of terms of the sequence {c(n)} defined in A218121.
%C A218123 It is easy to see that every prime is in the sequence.
%p A218123 ispfree := proc(a,b)
%p A218123     local alow ;
%p A218123     alow := floor(a);
%p A218123     if nextprime(alow) < b then
%p A218123         false;
%p A218123     else
%p A218123         true;
%p A218123     end if;
%p A218123 end proc:
%p A218123 A218121c := proc(n)
%p A218123     option remember;
%p A218123     local k ;
%p A218123     if n = 1 then
%p A218123         return 1;
%p A218123     elif n = 2 then
%p A218123         return 5/2 ;
%p A218123     else
%p A218123         if ispfree(ithprime(n)/procname(n-1),ithprime(n+1)/procname(n-1)) then
%p A218123             return procname(n-1) ;
%p A218123         end if ;
%p A218123         for k from n by -1 do
%p A218123             if ispfree( ithprime(n)*ithprime(k)/ithprime(n+1),ithprime(k) )
%p A218123                 and ithprime(n+1)/ithprime(k) > procname(n-1) then
%p A218123                 return ithprime(n+1)/ithprime(k) ;
%p A218123             end if;
%p A218123         end do:
%p A218123     end if;
%p A218123 end proc:
%p A218123 A218123 := proc(n)
%p A218123     denom(A218121c(n)) ;
%p A218123 end proc: # _R. J. Mathar_, Dec 02 2012
%Y A218123 Cf. A218121, A217871, A217689, A217691, A217833, A217884.
%K A218123 nonn,frac
%O A218123 1,2
%A A218123 _Vladimir Shevelev_, Oct 21 2012