A248196 - OEIS

%I #4 Oct 06 2014 23:01:22

%S 3,5,7,9,11,13,15,17,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,

%T 50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,87,89,91,93,

%U 95,97,99,101,103,105,107,109,111,113,115,117,119,121,123

%N Numbers k such that A248180(k+1) = A248180(k) + 1.

%C Complement of A248195.

%H Clark Kimberling, <a href="/A248196/b248196.txt">Table of n, a(n) for n = 0..1500</a>

%e The difference sequence of A248180 is (0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1,...), so that A248195 = (1,2,4,6,8,10,12,14,16,19,...) and A248196 = (3,5,7,9,11,13,15,17,18,...)

%t $MaxExtraPrecision = Infinity;

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

%t r = Sum[1/Binomial[2 h + 1, h], {h, 0, Infinity}]  (* A248179 *)

%t r = 2/27 (9 + 2 Sqrt[3] \[Pi]); N[r, 20]

%t N[Table[r - p[n], {n, 0, z/10}]]

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

%t u = Flatten[Table[f[n], {n, 0, z}]]  (* A248180 *)

%t Flatten[Position[Differences[u], 0]] (* A248195 *)

%t Flatten[Position[Differences[u], 1]] (* A248196 *)

%Y Cf. A248180, A248195.

%K nonn,easy

%O 0,1

%A _Clark Kimberling_, Oct 03 2014