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

1,5

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).

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)

Example

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.

Prog

(C++) See Links section.

Crossrefs

Cf. A276204, A289814.

Sequence in context: A268811 A351192 A306460 * A231561 A113297 A119985

Adjacent sequences: A317802 A317803 A317804 * A317806 A317807 A317808

Keyword

nonn,base,look

Author

Rémy Sigrist, Aug 07 2018

Status

approved