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A305979 Filter sequence for a(Fermi-Dirac primes) = constant sequences.

%I A305979 #7 Jul 02 2018 20:25:19
%S A305979 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 A305979 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 A305979 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 A305979 Filter sequence for a(Fermi-Dirac primes) = constant sequences.
%C A305979 For all i, j:
%C A305979   a(i) = a(j) => A305976(i) = A305976(j).
%C A305979   a(i) = a(j) => A302791(i) = A302791(j).
%H A305979 Antti Karttunen, <a href="/A305979/b305979.txt">Table of n, a(n) for n = 1..100000</a>
%F A305979 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 A305979 (PARI)
%o A305979 up_to = 100000;
%o A305979 partialsums(f,up_to) = { my(v = vector(up_to), s=0); for(i=1,up_to,s += f(i); v[i] = s); (v); }
%o A305979 A209229(n) = (n && !bitand(n, n-1));
%o A305979 A302777(n) = A209229(isprimepower(n));
%o A305979 v302778 = partialsums(A302777,up_to);
%o A305979 A302778(n) = v302778[n];
%o A305979 A305979(n) = if(1==n,n,if(1==A302777(n),2,1+n-A302778(n)));
%Y A305979 Cf. A050376, A302777, A302778, A302791, A305975, A305976.
%K A305979 nonn
%O A305979 1,2
%A A305979 _Antti Karttunen_, Jul 02 2018