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A248567 Numbers k such that A248565(k+1) = A248565(k) + 2.

%I A248567 #4 Oct 15 2014 21:00:56
%S A248567 3,6,9,11,13,16,18,20,22,24,26,28,31,33,35,37,39,41,43,45,47,49,51,53,
%T A248567 55,57,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,
%U A248567 100,102,104,106,108,110,112,114,117,119,121,123,125,127,129
%N A248567 Numbers k such that A248565(k+1) = A248565(k) + 2.
%H A248567 Clark Kimberling, <a href="/A248567/b248567.txt">Table of n, a(n) for n = 1..500</a>
%e A248567 (A248565(k+1) - A248565(k)) = (1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2,...), so that A248566 = (1, 2, 4, 5, 7, 8, 10, 12, 14, ..) and A248567 = (3, 6, 9, 11, 13, 16, 18, 20, ...).
%t A248567 z = 2500; p[k_] := p[k] = Sum[1/(h*4^h), {h, 1, k}];
%t A248567 N[Table[p[k], {k, 1, z/5}], 12];
%t A248567 N[Table[Log[4/3] - p[n], {n, 1, z/5}]];
%t A248567 f[n_] := f[n] = Select[Range[z], Log[4/3] - p[#] < 1/8^n &, 1];
%t A248567 u = Flatten[Table[f[n], {n, 1, z}]] ;   (* A248565 *)
%t A248567 Flatten[Position[Differences[u], 1]];   (* A248566 *)
%t A248567 Flatten[Position[Differences[u], 2]];   (* A248567 *)
%Y A248567 Cf. A248565, A248566, A248561, A248564.
%K A248567 nonn,easy
%O A248567 1,1
%A A248567 _Clark Kimberling_, Oct 09 2014