A341910 Lexicographically earliest sequence of distinct nonnegative integers such that for any n >= 0, the number of runs in the binary expansion of n equals the number of ones in the binary expansion of a(n).
0, 1, 3, 2, 5, 7, 6, 4, 9, 11, 15, 13, 10, 14, 12, 8, 17, 19, 23, 21, 27, 31, 29, 22, 18, 25, 30, 26, 20, 28, 24, 16, 33, 35, 39, 37, 43, 47, 45, 38, 46, 55, 63, 59, 51, 61, 53, 41, 34, 42, 54, 44, 57, 62, 58, 49, 36, 50, 60, 52, 40, 56, 48, 32, 65, 67, 71, 69
Offset: 0
Examples
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 5 100 101 5 7 101 111 6 6 110 110 7 4 111 100 8 9 1000 1001 9 11 1001 1011 10 15 1010 1111
Links
- Rémy Sigrist, Table of n, a(n) for n = 0..8191
- Rémy Sigrist, Colored scatterplot of the first 2^16 terms (where the color is function of A005811(n))
- Rémy Sigrist, PARI program for A341910
- Rémy Sigrist, PARI program for A341910 (faster)
- Index entries for sequences related to binary expansion of n
- Index entries for sequences that are permutations of the natural numbers
Programs
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Mathematica
Block[{a = {0}, k}, Do[k = 1; While[Nand[FreeQ[a, k], DigitCount[k, 2, 1] == #], k++] &@ Length[Split@ IntegerDigits[i, 2]]; AppendTo[a, k], {i, 67}]; a] (* Michael De Vlieger, Feb 24 2021 *) -
PARI
See Links section.
Comments