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A228540
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Rows of negated binary Walsh matrices interpreted as reverse binary numbers.
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4
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1, 3, 1, 15, 5, 3, 9, 255, 85, 51, 153, 15, 165, 195, 105, 65535, 21845, 13107, 39321, 3855, 42405, 50115, 26985, 255, 43605, 52275, 26265, 61455, 23205, 15555, 38505, 4294967295, 1431655765, 858993459, 2576980377, 252645135, 2779096485, 3284386755
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OFFSET
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0,2
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COMMENTS
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T(n,k) is row k of the negated binary Walsh matrix of size 2^n read as reverse binary number. The left digit is always 1, so all entries are odd.
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 A228539.)
Divisibility by Fermat numbers:
All entries in rows n >= 1 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.
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LINKS
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FORMULA
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EXAMPLE
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Negated binary Walsh matrix of size 4 and row 2 of the triangle:
1 1 1 1 15
1 0 1 0 5
1 1 0 0 3
1 0 0 1 9
Triangle starts:
k = 0 1 2 3 4 5 6 7 8 9 10 11 ...
n
0 1
1 3 1
2 15 5 3 9
3 255 85 51 153 15 165 195 105
4 65535 21845 13107 39321 3855 42405 50115 26985 255 43605 52275 26265 ...
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CROSSREFS
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A228539 (the same for the binary Walsh matrix, not negated)
A197818 (antidiagonals of the negated binary Walsh matrix converted to decimal).
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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