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A342700
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For any number n with binary expansion (b(1), b(2), ..., b(k)), the binary expansion of a(n) is (1-floor((b(k)+b(1)+b(2))/2), 1-floor((b(1)+b(2)+b(3))/2), ..., 1-floor((b(k-1)+b(k)+b(1))/2)).
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3
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0, 0, 2, 0, 7, 0, 0, 0, 15, 6, 10, 0, 3, 0, 0, 0, 31, 14, 30, 12, 23, 4, 16, 0, 7, 6, 2, 0, 3, 0, 0, 0, 63, 30, 62, 28, 63, 28, 56, 24, 47, 14, 42, 8, 35, 0, 32, 0, 15, 14, 14, 12, 7, 4, 0, 0, 7, 6, 2, 0, 3, 0, 0, 0, 127, 62, 126, 60, 127, 60, 120, 56, 127, 62
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OFFSET
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0,3
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COMMENTS
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This sequence is a variant of A342698; here the value of the k-th bit of a(n) is the less frequent value in the bit triple centered around the k-th bit of n.
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LINKS
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FORMULA
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EXAMPLE
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The first terms, in decimal and in binary, are:
n a(n) bin(n) bin(a(n))
-- ---- ------ ---------
0 0 0 0
1 0 1 0
2 2 10 10
3 0 11 0
4 7 100 111
5 0 101 0
6 0 110 0
7 0 111 0
8 15 1000 1111
9 6 1001 110
10 10 1010 1010
11 0 1011 0
12 3 1100 11
13 0 1101 0
14 0 1110 0
15 0 1111 0
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PROG
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(PARI) a(n) = my (w=#binary(n)); sum(k=0, w-1, ((bittest(n, (k-1)%w)+bittest(n, k%w)+bittest(n, (k+1)%w))<=1) * 2^k)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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