A248629 -id:A248629 - cp's OEIS frontend

A248630 Numbers k such that A248630(k+1) = A248360(k) + 1.

7, 11, 15, 18, 22, 25, 28, 31, 34, 37, 39, 42, 45, 48, 51, 53, 56, 59, 61, 64, 67, 69, 72, 75, 77, 80, 82, 85, 88, 90, 93, 95, 98, 101, 103, 106, 108, 111, 113, 116, 118, 121, 124, 126, 129, 131, 134, 136, 139, 141, 144, 146, 149, 151, 154, 156, 159, 161

Offset: 1

Clark Kimberling, Oct 10 2014

			(A248630(k+1) = A248360(k)) = (2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 2, 1, 2, 2, 1, ...), so that A248630 = (7, 11, 15, 18, ...).

Clark Kimberling, Table of n, a(n) for n = 1..500

Cf. A248630, A248629, A248632.

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 *)

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

Original entry on oeis.org

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 *)

A248631 Least k such that 3/2 - sum{(h^2)/3^h, h = 1..k} < 1/2^n.

Original entry on oeis.org

3, 4, 5, 6, 7, 8, 8, 9, 10, 11, 11, 12, 13, 14, 14, 15, 16, 16, 17, 18, 19, 19, 20, 21, 21, 22, 23, 23, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 31, 31, 32, 33, 33, 34, 35, 35, 36, 37, 37, 38, 39, 39, 40, 41, 41, 42, 43, 43, 44, 45, 45, 46, 47, 47, 48, 49, 49

Offset: 1

Clark Kimberling, Oct 11 2014

This sequence provides insight into the manner of convergence of sum{(h^2)/3^h, h = 1..k} to 3/2.

			Let s(n) = 3/2 - sum{(h^2)/3^h, h = 1..n}.  Approximations follow:
n ... s(n) ...... 1/2^n
1 ... 1.16666 ... 0.500000
2 ... 0.72222 ... 0.250000
3 ... 0.38888 ... 0.125000
4 ... 0.03909 ... 0.062500
5 ... 0.08847 ... 0.031250
6 ... 0.03909 ... 0.015625
7 ... 0.01668 ... 0.007812
a(5) = 7 because s(7) < 1/32 < s(6).

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

Cf. A248632, 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 *)

cp's OEIS Frontend

A248630 Numbers k such that A248630(k+1) = A248360(k) + 1.

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

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A248631 Least k such that 3/2 - sum{(h^2)/3^h, h = 1..k} < 1/2^n.

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