login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A228539 Rows of binary Walsh matrices interpreted as reverse binary numbers. 5
0, 0, 2, 0, 10, 12, 6, 0, 170, 204, 102, 240, 90, 60, 150, 0, 43690, 52428, 26214, 61680, 23130, 15420, 38550, 65280, 21930, 13260, 39270, 4080, 42330, 49980, 27030, 0, 2863311530, 3435973836, 1717986918, 4042322160, 1515870810, 1010580540 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
T(n,k) is row k of the binary Walsh matrix of size 2^n read as reverse binary number. The left digit is always 0, so all entries are even.
Most of these numbers are divisible by Fermat numbers (A000215): All entries in all rows beginning with row n are divisible by F_(n-1), except the entries 2^(n-1)...2^n-1. (This is the same in A228540.)
Divisibility by Fermat numbers:
All entries are divisible by F_0 = 3, except those with k = 1.
All entries in rows n >= 3 are divisible by F_2 = 17, except those with k = 4..7.
LINKS
Tilman Piesk, Prime factorizations
FORMULA
T(n,k) + A228540(n,k) = 2^2^n - 1
T(n,2^n-1) = A122570(n+1)
EXAMPLE
Binary Walsh matrix of size 4 and row 2 of the triangle:
0 0 0 0 0
0 1 0 1 10
0 0 1 1 12
0 1 1 0 6
Triangle starts:
k = 0 1 2 3 4 5 6 7 8 9 10 11 ...
n
0 0
1 0 2
2 0 10 12 6
3 0 170 204 102 240 90 60 150
4 0 43690 52428 26214 61680 23130 15420 38550 65280 21930 13260 39270 ...
CROSSREFS
Cf. A228540 (the same for the negated binary Walsh matrix).
Cf. A000215 (Fermat numbers), A023394 (Prime factors of Fermat numbers).
Sequence in context: A303350 A351879 A070681 * A061189 A019220 A019140
KEYWORD
nonn,tabf
AUTHOR
Tilman Piesk, Aug 24 2013
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 20 08:38 EDT 2024. Contains 373515 sequences. (Running on oeis4.)