|
%I #17 Feb 03 2024 19:51:33
%S 0,1,2,3,10,15,41,63,162,381,847,1485,3301,5811,12910,27823,58650,
%T 109293,230963,430103,910595,1898711,3913703,7507637,15505589,
%U 31746650,64574876,130712028,263644132,520381365,1050777736,2071510458,4187373082,8439258405,16971077851
%N a(n) = number of nonempty subsets S of {1,2,...,n} such that (number of primes in S) <= (number of nonprimes in S).
%H Alois P. Heinz, <a href="/A369781/b369781.txt">Table of n, a(n) for n = 0..2000</a>
%F a(n) + A369780(n) = 2^n-1 = A369853(n) + A369854(n).
%e a(4) = 10 enumerates these subsets: {1}, {4}, {1,2}, {1,3}, {1,4}, {2,4}, {3,4}, {1,3,4}, {1,2,4}, {1,2,3,4}.
%t Map[Length[Select[Map[Commonest, PrimeQ[Rest[Subsets[Range[#]]]]], # != {True} &]] &, Range[22]] (* _Peter J. C. Moses_, Jan 29 2024 *)
%Y Cf. A000040, A018252, A037031, A369781, A369853, A369854.
%K nonn
%O 0,3
%A _Clark Kimberling_, Feb 03 2024
%E a(23)-a(34) from _Alois P. Heinz_, Feb 03 2024
|
