cp's OEIS Frontend

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).

%I A286417 #16 May 10 2017 23:59:59
%S A286417 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,
%T A286417 39,43,22,24,31,32,34,69,37,75,78,35,41,45,44,53,47,48,49,71,52,27,28,
%U A286417 50,58,55,30,59,64,65,33,67,138,70,141,73,38,77,57,61,82
%N 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).
%C A286417 This sequence is a permutation of the natural numbers.
%C A286417 As for A160855, the scatterplot of this sequence shows (almost) straight lines:
%C A286417 - here those lines are related to the position of a(n) in the n-th prime (in binary representation),
%C A286417 - 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,
%C A286417 - see also the scatterplots in the Links section.
%C A286417 For any n>0, a(n) <= A000040(n); the first known values where equality occurs are a(2) = 3 and a(4) = 7.
%C A286417 The fixed points of the sequence belong to A091020.
%C A286417 The first fixed points are: 1, 5, 6, 31, 32, 50, 81, 1052, 3378.
%H A286417 Rémy Sigrist, <a href="/A286417/b286417.txt">Table of n, a(n) for n = 1..10000</a>
%H A286417 Rémy Sigrist, <a href="/A286417/a286417.pdf">Illustration of the first terms</a>
%H A286417 Rémy Sigrist, <a href="/A286417/a286417.png">Colorized scatterplot of the first 100000 terms</a>
%H A286417 Rémy Sigrist, <a href="/A286417/a286417_1.png">Scatterplot of the numbers appearing in the binary representation of the first 10000 prime numbers (this scatterplot contains the scatterplot of a)</a>
%H A286417 Rémy Sigrist, <a href="/A286417/a286417_1.gp.txt">PARI program for A286417</a>
%H A286417 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A286417 See illustration of the first terms in the Links section.
%Y A286417 Cf. A000040, A091020, A160855.
%K A286417 nonn,base,look
%O A286417 1,2
%A A286417 _Rémy Sigrist_, May 08 2017