A248631 -id:A248631 - cp's OEIS frontend

A248632 Numbers k such that A248631(k+1) = A248631(k).

6, 10, 14, 17, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 77, 80, 83, 86, 89, 92, 95, 97, 100, 103, 106, 109, 111, 114, 117, 120, 123, 126, 128, 131, 134, 137, 140, 142, 145, 148, 151, 154, 156, 159, 162, 165, 168, 170, 173

Offset: 1

Clark Kimberling, Oct 11 2014

			(A248631(k+1) = A248631(k)) = (1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1,... ), so that A248632 = (6, 10, 14, ... ).

Clark Kimberling, Table of n, a(n) for n = 1..300

Cf. A248631, A248630.

z = 200; p[k_] := p[k] = Sum[(h^2/2^h), {h, 1, k}];
d = N[Table[6 - p[k], {k, 1, z/5}], 12];
f[n_] := f[n] = Select[Range[z], 6 - p[#] < 1/3^n &, 1];
u = Flatten[Table[f[n], {n, 1, z}]]; (* A248629 *)
d = Differences[u];
Flatten[Position[d, 1]];  (* A248630 *)

A248629 Least k such that 6 - sum{(h^2)/2^h, h = 1..k} < 1/3^n.

Original entry on oeis.org

9, 11, 13, 15, 17, 19, 21, 22, 24, 26, 28, 29, 31, 33, 35, 36, 38, 40, 41, 43, 45, 47, 48, 50, 52, 53, 55, 57, 58, 60, 62, 63, 65, 67, 68, 70, 72, 73, 75, 76, 78, 80, 81, 83, 85, 86, 88, 90, 91, 93, 95, 96, 98, 99, 101, 103, 104, 106, 108, 109, 111, 112, 114

Offset: 1

Clark Kimberling, Oct 10 2014

This sequence provides insight into the manner of convergence of sum{(h^2)/2^h, h = 1..k} to 6.

			Let s(n) = 6 - sum{(h^2)/2^h, h = 1..n}.  Approximations follow:
n ... s(n) ........ 1/3^n
1 ... 5.50000 ... 0.333333
2 ... 4.50000 ... 0.111111
3 ... 3.37500 ... 0.037037
4 ... 2.37500 ... 0.012345
5 ... 1.59375 ... 0.004115
6 ... 1.03125 ... 0.001371
7 ... 0.64843 ... 0.000457
8 ... 0.39843 ... 0.000152
9 ... 0.24023 ... 0.000050
10 .. 0.14257 ... 0.000018
11 .. 0.08349 ... 0.000006
a(2) = 11 because s(11) < 1/9 < s(10).

Clark Kimberling, Table of n, a(n) for n = 1..1000

Cf. A248630, A248631.

z = 300; p[k_] := p[k] = Sum[(h^2/2^h), {h, 1, k}]
d = N[Table[6 - p[k], {k, 1, z/5}], 12]
f[n_] := f[n] = Select[Range[z], 6 - p[#] < 1/3^n &, 1]
u = Flatten[Table[f[n], {n, 1, z}]]  (* A248629 *)
d = Differences[u]
v = Flatten[Position[d, 1]]  (* A248630 *)

cp's OEIS Frontend

A248632 Numbers k such that A248631(k+1) = A248631(k).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica