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1, 1, 3, 1, 3, 1, 7, 1, 3, 1, 7, 1, 3, 1, 15, 1, 3, 1, 7, 1, 3, 1, 15, 1, 3, 1, 7, 1, 3, 1, 31, 1, 3, 1, 7, 1, 3, 1, 15, 1, 3, 1, 7, 1, 3, 1, 31, 1, 3, 1, 7, 1, 3, 1, 15, 1, 3, 1, 7, 1, 3, 1, 63, 1, 3, 1, 7, 1, 3, 1, 15, 1, 3, 1, 7, 1, 3, 1, 31, 1, 3, 1, 7, 1, 3, 1, 15, 1, 3, 1, 7, 1, 3, 1, 63, 1, 3, 1, 7, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,3
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LINKS
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Table of n, a(n) for n=1..100.
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EXAMPLE
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Contribution from Omar E. Pol, Mar 11 2011 (Start):
Can be written as a triangle with 2^k entries on each row:
1,
1,3,
1,3,1,7,
1,3,1,7,1,3,1,15,
1,3,1,7,1,3,1,15,1,3,1,7,1,3,1,31,
1,3,1,7,1,3,1,15,1,3,1,7,1,3,1,31,1,3,1,7,1,3,1,15,1,3, 1,7,1,3,1,63,
Last term of rows are 2^(k+1) - 1. It appears that the row sums give A001787.
(End)
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MAPLE
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GS(2, 6, 200); [see A135416].
# Input n is the number of rows.
A135521_list := proc(n) local i, k, NimSum;
NimSum := proc(a, b) option remember; local i;
zip((x, y)->`if`(x<>y, 1, 0), convert(a, base, 2), convert(b, base, 2), 0);
add(`if`(%[i]=1, 2^(i-1), 0), i=1..nops(%)) end:
seq(seq(NimSum(i, i+1), i=0..2^k-1), k=0..n) end:
A135521_list(5); # - Peter Luschny, May 31 2011
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MATHEMATICA
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Flatten[Table[BitXor[i, i + 1], {k, 0, 10}, {i, 0, -1 + 2^k}]] - Peter Luschny, May 31 2011
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CROSSREFS
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Cf. A135416, A091090.
This is Guy Steele's sequence GS(2, 6) (see A135416).
Cf. A000225, A001787. - Omar E. Pol, Mar 11 2011
Sequence in context: A066637 A050336 A095250 * A176032 A218403 A122410
Adjacent sequences: A135518 A135519 A135520 * A135522 A135523 A135524
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KEYWORD
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nonn,tabf
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AUTHOR
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N. J. A. Sloane, based on a message from Guy Steele and D. E. Knuth, Mar 01 2008
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STATUS
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approved
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