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

Author

Rémy Sigrist, May 08 2017

Keywords

• nonn
• base
• look

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.

Examples

			See illustration of the first terms in the Links section.
		

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

Crossrefs

Cf. A000040, A091020, A160855.