A036296 Denominator of Sum_{i=1..n} i/2^i.

1, 2, 1, 8, 8, 32, 8, 128, 128, 512, 256, 2048, 2048, 8192, 1024, 32768, 32768, 131072, 65536, 524288, 524288, 2097152, 524288, 8388608, 8388608, 33554432, 16777216, 134217728, 134217728, 536870912, 33554432, 2147483648, 2147483648, 8589934592, 4294967296

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• frac
• easy

Comments

Sum_{i>=0} i/2^i = 2. - Alonso del Arte, Aug 15 2012

Examples

			a(4) = 8 because 1/2 + 2/4 + 3/8 + 4/16 = 1/2 + 1/2 + 3/8 + 1/4 = 1 + 5/8 = 13/8.
		

References

• C. C. Clawson, The Beauty and Magic of Numbers. New York: Plenum Press (1996): 95.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• A. F. Horadam, Oresme numbers, Fib. Quart., 12 (1974), 267-271.

Crossrefs

Cf. A036295 (numerators).

Cf. A000079, A006519.

Programs

Magma

[1] cat [Denominator(&+[i/2^i: i in [1..n]]): n in [1..40]]; // Vincenzo Librandi, Nov 09 2014

Maple

seq(denom(2-(n+2)/2^n), n=0..50); # Ridouane Oudra, Jul 16 2023

Mathematica

Table[Denominator[Sum[i/2^i, {i, n}]], {n, 40}] (* Alonso del Arte, Aug 08 2012 *)

PARI

concat(1, vector(100, n, denominator(sum(i=1, n, i/2^i)))) \\ Colin Barker, Nov 09 2014

PARI

a(n) = denominator(2-(n+2)/2^n); \\ Joerg Arndt, Jul 17 2023

Formula

a(n) = denominator(2-(n+2)/2^n). - Sean A. Irvine, Oct 25 2020

a(n) = A000079(n)/A006519(n+2), for n>=1. - Ridouane Oudra, Jul 16 2023

Denominators of coefficients in expansion of 2*x / ((1 - x) * (2 - x)^2). - Ilya Gutkovskiy, Aug 04 2023