A317805 Lexicographically earliest sequence of nonnegative terms such that for any n > 0 and k > 0, a(n) AND a(n + k) <> a(n + 2*k) (where AND denotes the bitwise AND operator).

0, 0, 1, 1, 2, 1, 1, 2, 2, 3, 3, 1, 3, 3, 4, 2, 4, 4, 3, 3, 5, 3, 3, 5, 2, 2, 1, 4, 4, 5, 5, 6, 5, 5, 6, 6, 3, 3, 6, 3, 3, 7, 5, 6, 7, 5, 6, 3, 7, 7, 8, 7, 8, 8, 9, 9, 7, 9, 9, 7, 7, 10, 10, 9, 9, 7, 7, 9, 10, 10, 6, 5, 10, 6, 5, 7, 11, 4, 7, 6, 7, 5, 9, 9, 11

Offset: 1

Author

Rémy Sigrist, Aug 07 2018

Keywords

• nonn
• base
• look

Comments

This sequence has similarities with A276204: here we consider the bitwise AND operator, there the addition operator.

Apparently, the variant where we use the bitwise OR operator corresponds, up to a change of offset, to A289814.

The scatterplot of the sequence has fractal features (see illustrations in Links section).

Examples

			For n = 10:
- a(10-2*1) AND a(10-1) = 2 AND 2 = 2,
- a(10-2*2) AND a(10-2) = 1 AND 2 = 0,
- a(10-2*3) AND a(10-3) = 1 AND 1 = 1,
- a(10-2*4) AND a(10-4) = 0 AND 1 = 0,
- hence a(10) = 3.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, C++ program for A317805
• Rémy Sigrist, Scatterplot of the first 9000000 terms
• Rémy Sigrist, Colored scatterplot of the first 9000000 terms (where the color is function of the greatest p such that floor(a(n)/2^p) == 1 mod 4 and n + b(a(n)) >= 2 * b(ceil(n/2^p)*2^p) and b(k) is the least m such that a(m) = k)

Crossrefs

Cf. A276204, A289814.