cp's OEIS Frontend

A303075 Lexicographically earliest sequence of distinct positive terms such that for any n > 0, the binary digits of a(n) appear in order but not necessarily as consecutive digits in the binary representation of the n-th prime number.

%I A303075 #13 May 03 2018 11:21:28
%S A303075 1,3,2,7,5,6,4,9,11,13,15,8,10,19,23,12,14,29,16,17,18,31,20,21,24,25,
%T A303075 27,26,22,28,63,32,33,34,35,37,30,40,39,38,41,42,47,48,49,51,43,55,56,
%U A303075 50,52,59,57,61,64,65,45,67,36,44,69,53,73,71,46,62,75
%N A303075 Lexicographically earliest sequence of distinct positive terms such that for any n > 0, the binary digits of a(n) appear in order but not necessarily as consecutive digits in the binary representation of the n-th prime number.
%C A303075 This sequence is a permutation of the natural numbers with inverse A303076.
%C A303075 This sequence has similarities with A286417; there binary digits have to be consecutive, here not.
%H A303075 Rémy Sigrist, <a href="/A303075/b303075.txt">Table of n, a(n) for n = 1..10000</a>
%H A303075 Rémy Sigrist, <a href="/A303075/a303075.gp.txt">PARI program for A303075</a>
%H A303075 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H A303075 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A303075 a(n) <= A000040(n).
%e A303075 The first terms, alongside the binary representations of the n-th prime and of a(n), are:
%e A303075   n   a(n)  bin(p_n)    bin(a(n))
%e A303075   --  ----  --------    ---------
%e A303075    1     1        10        1_
%e A303075    2     3        11        11
%e A303075    3     2       101       10_
%e A303075    4     7       111       111
%e A303075    5     5      1011      101_
%e A303075    6     6      1101      110_
%e A303075    7     4     10001     100__
%e A303075    8     9     10011     1001_
%e A303075    9    11     10111     1011_
%e A303075   10    13     11101     11_01
%e A303075   11    15     11111     1111_
%e A303075   12     8    100101    100_0_
%e A303075   13    10    101001    1010__
%e A303075   14    19    101011    10_011
%e A303075   15    23    101111    10111_
%o A303075 (PARI) See Links section.
%Y A303075 Cf. A000040, A286417, A303076 (inverse).
%K A303075 nonn,base,look
%O A303075 1,2
%A A303075 _Rémy Sigrist_, Apr 18 2018