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A342698
For any number n with binary expansion (b(1), b(2), ..., b(k)), the binary expansion of a(n) is (floor((b(k)+b(1)+b(2))/2), floor((b(1)+b(2)+b(3))/2), ..., floor((b(k-1)+b(k)+b(1))/2)).
4
0, 1, 1, 3, 0, 7, 7, 7, 0, 9, 5, 15, 12, 15, 15, 15, 0, 17, 1, 19, 8, 27, 15, 31, 24, 25, 29, 31, 28, 31, 31, 31, 0, 33, 1, 35, 0, 35, 7, 39, 16, 49, 21, 55, 28, 63, 31, 63, 48, 49, 49, 51, 56, 59, 63, 63, 56, 57, 61, 63, 60, 63, 63, 63, 0, 65, 1, 67, 0, 67, 7
OFFSET
0,4
COMMENTS
This sequence is a variant of A342697; here we deal with bit triples in a "cyclic" binary representation of n.
FORMULA
a(n) + A342700(n) = A003817(n).
a(n) = n iff n belongs to A342699.
EXAMPLE
The first terms, in decimal and in binary, are:
n a(n) bin(n) bin(a(n))
-- ---- ------ ---------
0 0 0 0
1 1 1 1
2 1 10 1
3 3 11 11
4 0 100 0
5 7 101 111
6 7 110 111
7 7 111 111
8 0 1000 0
9 9 1001 1001
10 5 1010 101
11 15 1011 1111
12 12 1100 1100
13 15 1101 1111
14 15 1110 1111
15 15 1111 1111
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))>=2) * 2^k)
CROSSREFS
Cf. A003817, A342697, A342699 (fixed points), A342700.
Sequence in context: A201900 A344387 A019970 * A239022 A343612 A363502
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Mar 18 2021
STATUS
approved