%I #7 Jul 02 2018 20:25:19
%S 1,2,2,2,2,3,2,4,2,5,2,6,2,7,8,2,2,9,2,10,11,12,2,13,2,14,15,16,2,17,
%T 2,18,19,20,21,22,2,23,24,25,2,26,2,27,28,29,2,30,2,31,32,33,2,34,35,
%U 36,37,38,2,39,2,40,41,42,43,44,2,45,46,47,2,48,2,49,50,51,52,53,2,54,2,55,2,56,57,58,59,60,2,61,62,63,64,65,66,67,2,68,69,70,2
%N Filter sequence for a(Fermi-Dirac primes) = constant sequences.
%C For all i, j:
%C a(i) = a(j) => A305976(i) = A305976(j).
%C a(i) = a(j) => A302791(i) = A302791(j).
%H Antti Karttunen, <a href="/A305979/b305979.txt">Table of n, a(n) for n = 1..100000</a>
%F a(1) = 1; for n > 1, if A302777(n) is 1 [when n is in A050376], a(n) = 2, otherwise a(n) = 1 + n - A302778(n) = running count from 3 onward.
%o (PARI)
%o up_to = 100000;
%o partialsums(f,up_to) = { my(v = vector(up_to), s=0); for(i=1,up_to,s += f(i); v[i] = s); (v); }
%o A209229(n) = (n && !bitand(n, n-1));
%o A302777(n) = A209229(isprimepower(n));
%o v302778 = partialsums(A302777,up_to);
%o A302778(n) = v302778[n];
%o A305979(n) = if(1==n,n,if(1==A302777(n),2,1+n-A302778(n)));
%Y Cf. A050376, A302777, A302778, A302791, A305975, A305976.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jul 02 2018