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A248638 Numbers k such that A248636(k+1) = A248636(k) + 1.

%I A248638 #4 Oct 17 2014 23:19:52
%S A248638 1,3,5,6,9,11,13,16,18,21,24,27,30,33,36,39,42,45,49,52,55,58,62,65,
%T A248638 68,72,75,79,82,85,89,92,96,99,103,106,110,113,117,120,124,127,131,
%U A248638 135,138,142,145,149,152,156,160,163,167,170,174,178,181,185,189
%N A248638 Numbers k such that A248636(k+1) = A248636(k) + 1.
%H A248638 Clark Kimberling, <a href="/A248638/b248638.txt">Table of n, a(n) for n = 1..400</a>
%e A248638 (A248636(k+1) = A248636(k)) = (2, 1, 2, 1, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2,... ), so that A248637 = (2, 4, 7, 8, 10, 12, 14, ... ) and A248638 = (1, 3, 5, 6, 9, 11, 13, ...).
%t A248638 z = 300; p[k_] := p[k] = Sum[(h^3/3^h), {h, 1, k}];
%t A248638 d = N[Table[33/8 - p[k], {k, 1, z/5}], 12]
%t A248638 f[n_] := f[n] = Select[Range[z], 33/8 - p[#] < 1/4^n &, 1];
%t A248638 u = Flatten[Table[f[n], {n, 1, z}]]  (* A248636 *)
%t A248638 d = Differences[u]
%t A248638 v = Flatten[Position[d, 1]] (* A248637 *)
%t A248638 w = Flatten[Position[d, 2]] (* A248638 *)
%Y A248638 Cf. A248636, A248637.
%K A248638 nonn,easy
%O A248638 1,2
%A A248638 _Clark Kimberling_, Oct 11 2014