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A342697
For any number n with binary expansion Sum_{k >= 0} b(k) * 2^k, the binary expansion of a(n) is Sum_{k >= 0} floor((b(k) + b(k+1) + b(k+2))/2) * 2^k.
4
0, 0, 0, 1, 0, 1, 3, 3, 0, 0, 2, 3, 6, 7, 7, 7, 0, 0, 0, 1, 4, 5, 7, 7, 12, 12, 14, 15, 14, 15, 15, 15, 0, 0, 0, 1, 0, 1, 3, 3, 8, 8, 10, 11, 14, 15, 15, 15, 24, 24, 24, 25, 28, 29, 31, 31, 28, 28, 30, 31, 30, 31, 31, 31, 0, 0, 0, 1, 0, 1, 3, 3, 0, 0, 2, 3, 6
OFFSET
0,7
COMMENTS
The value of the k-th bit in a(n) corresponds to the most frequent value in the bit triple starting at the k-th bit in n.
FORMULA
a(n) = 0 iff n belongs to A048715.
a(n) = floor(A048730(n)/8) = floor(A048733(n)/2). - Kevin Ryde, Mar 26 2021
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 0 10 0
3 1 11 1
4 0 100 0
5 1 101 1
6 3 110 11
7 3 111 11
8 0 1000 0
9 0 1001 0
10 2 1010 10
11 3 1011 11
12 6 1100 110
13 7 1101 111
14 7 1110 111
15 7 1111 111
PROG
(PARI) a(n) = sum(k=0, #binary(n), ((bittest(n, k)+bittest(n, k+1)+bittest(n, k+2))>=2) * 2^k)
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Rémy Sigrist, Mar 18 2021
STATUS
approved