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A342700 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)). 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
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.
LINKS
FORMULA
a(n) + A342698(n) = A003817(n).
a(n) = n iff n belongs to A020988.
EXAMPLE
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
PROG
(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)
CROSSREFS
Cf. A003817, A020988 (fixed points), A342698.
Sequence in context: A294470 A283654 A291373 * A021487 A369745 A197391
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Mar 18 2021
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)