A359259 a(n) is the least k such that A359194(k) = A032766(n).

1, 0, 4, 9, 3, 8, 18, 7, 17, 6, 16, 37, 15, 36, 14, 35, 13, 34, 12, 33, 11, 32, 74, 31, 73, 30, 72, 29, 71, 28, 70, 27, 69, 26, 68, 25, 67, 24, 66, 23, 65, 22, 64, 149, 63, 148, 62, 147, 61, 146, 60, 145, 59, 144, 58, 143, 57, 142, 56, 141, 55, 140, 54, 139

Offset: 0

Author

Rémy Sigrist, Dec 23 2022

Keywords

• nonn
• base

Comments

The binary expansion of numbers m such that A359194(m) = A032766(n):

- starts with zero or more occurrences of "10",

- followed by a "0" when the binary expansion of a(n) starts with zero or more occurrences of "10" followed by "11",

- ends with the binary expansion of a(n) (assuming that 0 has an empty binary expansion).

Examples

			The first terms, alongside the binary expansions of A032766(n) and a(n), are:
  n   a(n)  bin(A032766(n))  bin(a(n))
  --  ----  ---------------  ---------
   0     1                0          1
   1     0                1          0
   2     4               11        100
   3     9              100       1001
   4     3              110         11
   5     8              111       1000
   6    18             1001      10010
   7     7             1010        111
   8    17             1100      10001
   9     6             1101        110
  10    16             1111      10000
  11    37            10000     100101
		

Crossrefs

Cf. A032766, A359194.

Programs

PARI

a(n) = { if (n<=1, return (1-n), n+=n\2; for (x=2+exponent(n), oo, my (k=bitneg(n,x)); if (k%3==0, return (k/3)))) }