A286417 Lexicographically earliest sequence of distinct positive terms such that the binary representation of the n-th prime contains the binary representation of a(n).

1, 3, 2, 7, 5, 6, 4, 9, 11, 13, 15, 18, 10, 21, 23, 26, 14, 29, 8, 17, 36, 19, 20, 12, 16, 25, 39, 43, 22, 24, 31, 32, 34, 69, 37, 75, 78, 35, 41, 45, 44, 53, 47, 48, 49, 71, 52, 27, 28, 50, 58, 55, 30, 59, 64, 65, 33, 67, 138, 70, 141, 73, 38, 77, 57, 61, 82

Offset

1,2

Comments

This sequence is a permutation of the natural numbers.

As for A160855, the scatterplot of this sequence shows (almost) straight lines:

- here those lines are related to the position of a(n) in the n-th prime (in binary representation),

- the scatterplot of the possible values of a(n) as a function of the n-th prime constitutes a network of lines in which the scatterplot of a(n) lies,

- see also the scatterplots in the Links section.

For any n>0, a(n) <= A000040(n); the first known values where equality occurs are a(2) = 3 and a(4) = 7.

The fixed points of the sequence belong to A091020.

The first fixed points are: 1, 5, 6, 31, 32, 50, 81, 1052, 3378.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Illustration of the first terms

Rémy Sigrist, Colorized scatterplot of the first 100000 terms

Rémy Sigrist, Scatterplot of the numbers appearing in the binary representation of the first 10000 prime numbers (this scatterplot contains the scatterplot of a)

Rémy Sigrist, PARI program for A286417

Index entries for sequences that are permutations of the natural numbers

Example

See illustration of the first terms in the Links section.

Crossrefs

Cf. A000040, A091020, A160855.

Sequence in context: A163915 A163916 A303075 * A303076 A298847 A059894

Adjacent sequences: A286414 A286415 A286416 * A286418 A286419 A286420

Keyword

nonn,base,look

Author

Rémy Sigrist, May 08 2017

Status

approved