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A194798 Numbers n having the same parity as the number of partitions of n.

%I A194798 #45 Jun 27 2016 18:24:50
%S A194798 1,2,3,5,7,8,10,13,17,22,23,26,28,29,30,33,34,35,37,39,40,41,42,43,46,
%T A194798 49,50,51,53,58,61,62,63,64,66,67,69,70,71,73,74,77,78,80,81,83,84,85,
%U A194798 86,87,89,91,93,94,95,96,98,99,100,105,106,107,108,110,111
%N A194798 Numbers n having the same parity as the number of partitions of n.
%C A194798 Odd positive integers with an odd number of partitions and even positive integers with an even number of partitions. - Omar E. Pol, Mar 17 2012
%C A194798 Union of A067567 and A127219. Note that the union of A163096 and A163097 gives A209920 and the union of A209920 and this sequence gives A001477. - Omar E. Pol, Mar 22 2012
%H A194798 Alois P. Heinz, <a href="/A194798/b194798.txt">Table of n, a(n) for n = 1..1000</a>
%H A194798 K. Ono, <a href="http://www.ams.org/era/1995-01-01/S1079-6762-95-01005-5/S1079-6762-95-01005-5.pdf">Parity of the partition function</a>, Electronic Research Announcements of AMS, Vol. 1, 1995, pp. 35-42; MR 96d:11108
%e A194798 10 is in the sequence because the number of partitions of 10 is equal to 42 and both 10 and 42 have the same parity.
%p A194798 with(combinat):
%p A194798 a:= proc(n) option remember; local k;
%p A194798       for k from 1+`if`(n=1, 0, a(n-1))
%p A194798       while irem(k+numbpart(k), 2)=1 do od; k
%p A194798     end:
%p A194798 seq(a(n), n=1..80); # _Alois P. Heinz_, Mar 16 2012
%t A194798 Select[Range[200], Mod[PartitionsP[#] - #, 2] == 0 &] (* _T. D. Noe_, Mar 16 2012 *)
%Y A194798 Cf. A000041, A040051, A052001, A052003, A067567, A127219, A154795-A154798, A163096, A163097, A163998, A194807, A209658, A209659, A209920.
%K A194798 nonn,easy
%O A194798 1,2
%A A194798 _Omar E. Pol_, Jan 29 2012
%E A194798 More terms from _Alois P. Heinz_, Mar 16 2012