A076827 Number of odd terms minus number of even terms in the set S(n) = ( A002977(k) : k<=n).

1, 2, 1, 2, 3, 2, 3, 4, 5, 6, 5, 6, 5, 6, 7, 6, 7, 8, 7, 8, 9, 8, 9, 8, 9, 10, 11, 10, 11, 12, 13, 14, 13, 14, 15, 16, 15, 16, 17, 18, 17, 18, 17, 18, 19, 20, 21, 20, 21, 20, 21, 22, 23, 24, 23, 24, 23, 24, 25, 26, 27, 26, 27, 26, 27, 28, 27, 28, 29, 28, 29, 30, 29, 30, 29, 30, 31

Offset: 1

Author

Benoit Cloitre, Nov 20 2002

Keywords

• nonn

Examples

			S(12) = (1,3,4,7,9,10,13,15,19,21,22,27) and there are 9 odd terms and 3 even terms in S(12), hence a(12) = 9-3 = 6.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Amiram Eldar, Plot of a(n)/n for n = 1000..10000

Crossrefs

Cf. A002977.

Programs

Mathematica

seq[max_] := Module[{s = Flatten[NestWhileList[Flatten[{2*# + 1, 3*# + 1}] &, 1, Min[#1] < max &]], t}, t = Union[Select[s, # <= max &]]; FoldList[Plus, -(-1)^t]]; seq[300] (* Amiram Eldar, May 07 2022 *)

Formula

a(n) = (-1)*Sum_{k=1..n} (-1)^A002977(k).

a(n) > 0 and a(n) seems to be asymptotic to c*n where c = 0.4...