A306696 Lexicographically earliest sequence of nonnegative terms such that for any n > 0 and k > 0, if a(n) >= a(n+k), then a(n+2*k) <> a(n+k).

0, 0, 1, 0, 1, 1, 2, 0, 2, 1, 3, 1, 2, 2, 3, 0, 3, 2, 4, 1, 3, 3, 4, 1, 4, 2, 5, 2, 4, 3, 5, 0, 5, 3, 6, 2, 4, 4, 6, 1, 5, 3, 7, 3, 5, 4, 6, 1, 6, 4, 7, 2, 5, 5, 7, 2, 6, 4, 8, 3, 6, 5, 7, 0, 7, 5, 8, 3, 6, 6, 8, 2, 7, 4, 9, 4, 7, 6, 8, 1, 8, 5, 9, 3, 7, 7, 9

Offset: 1

Author

Rémy Sigrist, Mar 05 2019

Keywords

• nonn

Comments

This sequence has graphical features in common with A286326.

Examples

			For n=1:
- a(1) = 0 is suitable.
For n=2:
- a(2) = 0 is suitable.
For n=3:
- a(1) = 0 >= a(2) = 0, so a(3) <> 0,
- a(3) = 1 is suitable.
For n=4:
- a(2) = 0 < a(3) = 1,
- a(4) = 0 is suitable.
For n=5:
- a(3) = 1 >= a(4) = 0, so a(5) <> 0,
- a(1) = 0 < a(3) = 1,
- a(5) = 1 is suitable.
For n=6:
- a(4) = 0 < a(5) = 1,
- a(2) = 0 >= a(4) = 0, so a(6) <> 0,
- a(6) = 1 is suitable.
For n=7:
- a(5) = 1 >= a(6) = 1, so a(7) <> 1,
- a(3) = 1 >= a(5) = 1, so a(7) <> 1,
- a(1) = 0 >= a(4) = 0, so a(7) <> 0,
- a(7) = 2 is suitable.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, C++ program for A306696
• Rémy Sigrist, Colored scatterplot of (n, a(n)) for n = 1..100000 (where the color is function of the least k >= 0 such that (1+a(n))/n >= 2^k/A007583(k))

Crossrefs

Cf. A000079, A007583, A164095, A181497, A286326.

Formula

Empirically:

- a(n) = 0 iff n is a power of 2 (A000079),

- a(n) = 1 iff n = 3 or belongs to A164095,

- a(2*n) = a(n),

- A181497(n) is the least k such that a(k) = n.