|
|
A036296
|
|
Denominator of Sum_{i=1..n} i/2^i.
|
|
4
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
COMMENTS
|
|
|
REFERENCES
|
C. C. Clawson, The Beauty and Magic of Numbers. New York: Plenum Press (1996): 95.
|
|
LINKS
|
|
|
FORMULA
|
Denominators of coefficients in expansion of 2*x / ((1 - x) * (2 - x)^2). - Ilya Gutkovskiy, Aug 04 2023
|
|
EXAMPLE
|
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.
|
|
MAPLE
|
|
|
MATHEMATICA
|
Table[Denominator[Sum[i/2^i, {i, n}]], {n, 40}] (* Alonso del Arte, Aug 08 2012 *)
|
|
PROG
|
(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
(Magma) [1] cat [Denominator(&+[i/2^i: i in [1..n]]): n in [1..40]]; // Vincenzo Librandi, Nov 09 2014
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,frac,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|