|
Search: id:A137284
|
|
|
| A137284 |
|
a(0)=1 and a(n) for n>0 equals the minimal positive integer such that addition of 2^(-a(n)) to Sum{ k = 0,1,...,n-1 } 2^(-a(k)) changes only tailing zeros in its decimal representation. |
|
+0
2
|
|
| 1, 4, 14, 47, 157, 522, 1735, 5764, 19148, 63609, 211305, 701941, 2331798, 7746066, 25731875, 85479439, 283956550, 943283242, 3133519104, 10409325148, 34579029658, 114869050115, 381586724811, 1267603661786, 4210888217270, 13988267873380, 46468020047392
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
First and last nonzero decimal digits of 2^(-m) appear respectively at the ceil(m/log2(10))-th and m-th positions after the point. Hence a(n+1) equals the minimum solution to ceil(x/log2(10))=a(n)+1, which is x = ceil(a(n)*log2(10)).
|
|
FORMULA
|
a(n+1) = ceil(a(n)*log2(10)) = ceil(a(n)*A020862). - Conjectured by R. J. Mathar, proved by Max Alekseyev.
|
|
EXAMPLE
|
Start from 0.
0 + 2^(-1)= 0.5
0.5 + 2^(-4)= 0.5625 (first digit "5" is equal to the decimal of prevoius number)
0.5625 + 2^(-14)=0.56256103515625 (first digits "5625" are equal to the decimals of prevoius number)
etc.
|
|
CROSSREFS
|
Sequence in context: A104487 A094789 A082574 this_sequence A121095 A000908 A015651
Adjacent sequences: A137281 A137282 A137283 this_sequence A137285 A137286 A137287
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Mar 14 2008
|
|
EXTENSIONS
|
Edited and extended by Max Alekseyev (maxale(AT)gmail.com), May 13 2009
|
|
|
Search completed in 0.002 seconds
|
