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 A228539 Rows of binary Walsh matrices interpreted as reverse binary numbers. 3
 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. 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 ... 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.) LINKS Tilman Piesk, Rows 0..8 of the triangle, flattened Tilman Piesk, Prime factorizations Tilman Piesk, Binary Walsh matrix of size 256 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 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. CROSSREFS A228540 (the same for the negated binary Walsh matrix). A000215 (Fermat numbers), A023394 (Prime factors of Fermat numbers). Sequence in context: A151887 A303350 A070681 * A061189 A019220 A019140 Adjacent sequences:  A228536 A228537 A228538 * A228540 A228541 A228542 KEYWORD nonn,tabf AUTHOR Tilman Piesk, Aug 24 2013 STATUS approved

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Last modified September 20 10:32 EDT 2019. Contains 327229 sequences. (Running on oeis4.)