A248609 - OEIS

%I #4 Oct 15 2014 21:01:37

%S 2,4,6,8,10,12,14,16,18,19,21,23,25,27,28,30,32,34,36,37,39,41,43,44,

%T 46,48,50,51,53,55,57,58,60,62,64,65,67,69,71,72,74,76,78,79,81,83,84,

%U 86,88,90,91,93,95,97,98,100,102,104,105,107,109,110,112

%N Numbers k such that A248607(k+1) = A248607(k) + 2.

%H Clark Kimberling, <a href="/A248609/b248609.txt">Table of n, a(n) for n = 1..500</a>

%e (A248607(k+1) - A248607(k)) = (1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 1, 2, 2,...), so that A248608 = (1, 3, 5, 7, 9, 11, 13, 15, 17, ..) and A248567 = (2, 4, 6, 8, 10, 12, 14, 16, ...).

%t z = 300; p[k_] := p[k] = Sum[2^h/((2 h + 1) Binomial[2 h, h]), {h, 0, k}]

%t d = N[Table[Pi/2 - p[k], {k, 1, z/5}], 12]

%t f[n_] := f[n] = Select[Range[z], Pi/2 - p[#] < 1/3^n &, 1]

%t u = Flatten[Table[f[n], {n, 1, z}]]  (* A248607 *)

%t d = Differences[u]

%t v = Flatten[Position[d, 1]] (* A248608 *)

%t w = Flatten[Position[d, 2]] (* A248609 *)

%Y Cf. A248607, A248608, A248611.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Oct 10 2014