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A341911
Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the number of ones in the binary expansion of n equals the number of runs in the binary expansion of a(n).
2
0, 1, 3, 2, 7, 4, 6, 5, 15, 8, 12, 9, 14, 11, 13, 10, 31, 16, 24, 17, 28, 19, 23, 18, 30, 25, 27, 20, 29, 22, 26, 21, 63, 32, 48, 33, 56, 35, 39, 34, 60, 47, 49, 36, 51, 38, 40, 37, 62, 55, 57, 44, 59, 46, 50, 41, 61, 52, 54, 43, 58, 45, 53, 42, 127, 64, 96
OFFSET
0,3
COMMENTS
This sequence is a permutation of the nonnegative integers with inverse A341910.
FORMULA
A000120(n) = A005811(a(n)).
a(n) < 2^k for any n < 2^k.
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 3 10 11
3 2 11 10
4 7 100 111
5 4 101 100
6 6 110 110
7 5 111 101
8 15 1000 1111
9 8 1001 1000
10 12 1010 1100
MATHEMATICA
Block[{a = {0}, k}, Do[k = 1; While[Nand[FreeQ[a, k], Length[Split@ IntegerDigits[k, 2]] == #], k++] &@ DigitCount[i, 2, 1]; AppendTo[a, k], {i, 66}]; a] (* Michael De Vlieger, Feb 24 2021 *)
PROG
(PARI) See Links section.
CROSSREFS
Cf. A000120, A005811, A298847, A341910 (inverse).
Sequence in context: A191664 A118319 A316385 * A341916 A360960 A371974
KEYWORD
nonn,look,base
AUTHOR
Rémy Sigrist, Feb 23 2021
STATUS
approved