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A194798
Numbers n having the same parity as the number of partitions of n.
6
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, 49, 50, 51, 53, 58, 61, 62, 63, 64, 66, 67, 69, 70, 71, 73, 74, 77, 78, 80, 81, 83, 84, 85, 86, 87, 89, 91, 93, 94, 95, 96, 98, 99, 100, 105, 106, 107, 108, 110, 111
OFFSET
1,2
COMMENTS
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
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
LINKS
K. Ono, Parity of the partition function, Electronic Research Announcements of AMS, Vol. 1, 1995, pp. 35-42; MR 96d:11108
EXAMPLE
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.
MAPLE
with(combinat):
a:= proc(n) option remember; local k;
for k from 1+`if`(n=1, 0, a(n-1))
while irem(k+numbpart(k), 2)=1 do od; k
end:
seq(a(n), n=1..80); # Alois P. Heinz, Mar 16 2012
MATHEMATICA
Select[Range[200], Mod[PartitionsP[#] - #, 2] == 0 &] (* T. D. Noe, Mar 16 2012 *)
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Jan 29 2012
EXTENSIONS
More terms from Alois P. Heinz, Mar 16 2012
STATUS
approved