Search: a214416 -id:a214416
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A105025
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Write numbers in binary under each other; to get the next block of 2^k (k >= 0) terms of the sequence, start at 2^k, read diagonals in downward direction and convert to decimal.
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+10
12
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0, 1, 3, 2, 4, 7, 6, 5, 11, 10, 9, 12, 15, 14, 13, 8, 18, 17, 20, 23, 22, 21, 16, 27, 26, 25, 28, 31, 30, 29, 24, 19, 33, 36, 39, 38, 37, 32, 43, 42, 41, 44, 47, 46, 45, 40, 35, 50, 49, 52, 55, 54, 53, 48, 59, 58, 57, 60, 63, 62, 61, 56, 51, 34, 68, 71, 70, 69, 64, 75, 74, 73, 76
(list;
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listen;
history;
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OFFSET
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0,3
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COMMENTS
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This is a permutation of the nonnegative integers.
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LINKS
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David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].
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EXAMPLE
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........0
........1
.......10
.......11
......100 <- Starting here, the downward diagonals
......101 read 100, 111, 110, 101, giving the block 4, 7, 6, 5.
......110
......111
.....1000
.....1001
.....1010
.....1011
.........
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MAPLE
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a:=proc(i, j) if j=1 and i<=16 then 0 else convert(i+15, base, 2)[7-j] fi end: seq(a(i, 2)*2^4+a(i+1, 3)*2^3+a(i+2, 4)*2^2+a(i+3, 5)*2+a(i+4, 6), i=1..16); # this is a Maple program (not necessarily the simplest) only for one block of (2^4) numbers # Emeric Deutsch, Apr 16 2005
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MATHEMATICA
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numberOfBlocks = 7; bloc[n_] := Join[ Table[ IntegerDigits[k, 2], {k, 2^(n-1), 2^n-1}], Table[ Rest @ IntegerDigits[k, 2], {k, 2^n, 2^n+n}]]; Join[{0, 1}, Flatten[ Table[ Table[ Diagonal[bloc[n], k] // FromDigits[#, 2]&, {k, 0, -2^(n-1)+1, -1}], {n, 2, numberOfBlocks}]]] (* Jean-François Alcover, Nov 03 2016 *)
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PROG
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(Haskell)
import Data.Bits ((.|.), (.&.))
a105025 n = foldl (.|.) 0 $ zipWith (.&.)
a000079_list $ reverse $ enumFromTo n (n - 1 + a070939 n)
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CROSSREFS
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KEYWORD
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nonn,nice,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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0, 1, 3, 2, 6, 5, 4, 7, 11, 10, 9, 12, 15, 14, 13, 8, 20, 19, 18, 21, 24, 23, 22, 17, 28, 27, 26, 29, 16, 31, 30, 25, 37, 36, 35, 38, 41, 40, 39, 34, 45, 44, 43, 46, 33, 48, 47, 42, 53, 52, 51, 54, 57, 56, 55, 50, 61, 60, 59, 62, 49, 32, 63, 58, 70, 69, 68
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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PROG
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(Haskell)
-- import Data.List (elemIndex)
-- import Data.Maybe (fromJust)
a214417 = fromJust . (`elemIndex` a105027_list)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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