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A371459
For any positive integer with binary digits (b_1, ..., b_w) (where b_1 = 1), the binary digits of a(n), possibly with leading zeros, are (b_2, b_4, ..., b_{floor(w/2) * 2}); a(0) = 0.
3
0, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 2, 3, 2, 3, 0, 0, 1, 1, 0, 0, 1, 1, 2, 2, 3, 3, 2, 2, 3, 3, 0, 1, 0, 1, 2, 3, 2, 3, 0, 1, 0, 1, 2, 3, 2, 3, 4, 5, 4, 5, 6, 7, 6, 7, 4, 5, 4, 5, 6, 7, 6, 7, 0, 0, 1, 1, 0, 0, 1, 1, 2, 2, 3, 3, 2, 2, 3, 3, 0, 0, 1, 1, 0, 0, 1
OFFSET
0,13
COMMENTS
In other words, we keep even-indexed bits.
Every integer appears infinitely many times in the sequence.
FORMULA
a(n) = 0 iff n belongs to A126684.
a(A000695(n)) = 0.
a(A001196(n)) = n.
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 0 101 0
6 1 110 1
7 1 111 1
8 0 1000 0
9 1 1001 1
10 0 1010 0
11 1 1011 1
12 2 1100 10
13 3 1101 11
14 2 1110 10
15 3 1111 11
16 0 10000 0
MATHEMATICA
A371459[n_] := FromDigits[IntegerDigits[n, 2][[2;; -1;; 2]], 2];
Array[A371459, 100, 0] (* Paolo Xausa, Mar 28 2024 *)
PROG
(PARI) a(n) = { my (b = binary(n)); fromdigits(vector(#b\2, k, b[2*k]), 2); }
(Python)
def A371459(n): return int(bin(n)[3::2], 2) if n>1 else 0 # Chai Wah Wu, Mar 27 2024
CROSSREFS
See A371442 for the sequence related to odd-indexed bits.
See A059906 and A063695 for similar sequences.
Sequence in context: A105436 A266911 A244075 * A354522 A059905 A295301
KEYWORD
nonn,base,easy
AUTHOR
Rémy Sigrist, Mar 24 2024
STATUS
approved