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%I #6 Mar 30 2012 17:34:13
%S 1,3,8,17,126,378,7604,38022,2075945,14531618,2156683401,23723517421,
%T 9570750010878,124419750141419,136442823568464604,2319528000663898268,
%U 6914415519745978746410,131373894875173596181802
%N An improved natural sequence based on two base scales Pi and e and the prime sequence.
%F a(n) = f_Pi[n]*f_E[n]
%t Phi=Pi Digits=40 (* Pi based sequence*) a=Table[If[m==0, Phi, Phi*Product[Prime[n], {n, 1, m}]], {m, 0, Digits}] (* one inserted to give one as first element*) a0=Insert[a, 1, 1] (* e based sequence*) b=Table[Exp[Sum[n, {n, 0, m}]], {m, 0, Digits}] c=Table[Floor[a0[[Floor[(n+1)/2]]]*b[[Floor[n/2]]]], {n, 2, Digits+1}]
%K nonn,uned
%O 0,2
%A _Roger L. Bagula_, Nov 20 2003