cp's OEIS Frontend

A288538 Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, n * a(n) does not contain the digit 1 in decimal base.

%I A288538 #18 Jun 26 2017 07:59:09
%S A288538 2,1,3,5,4,6,7,8,10,9,19,17,16,18,15,13,12,14,11,20,22,21,23,24,25,26,
%T A288538 27,28,30,29,32,31,62,59,58,57,55,54,52,50,49,53,48,46,45,44,47,43,41,
%U A288538 40,56,39,42,38,37,51,36,35,34,60,63,33,61,64,65,66,67
%N A288538 Lexicographically earliest sequence of distinct positive terms such that, for any n > 0, n * a(n) does not contain the digit 1 in decimal base.
%C A288538 This sequence is a permutation of the natural numbers; for any n > 0, there are infinitely many values v such that n * v does not contain the digit 1 in decimal base (for example: 2 * A004290(n) / n * 10^k for k = 0, 1, 2,...), hence n will eventually be chosen.
%C A288538 This sequence is self-inverse.
%C A288538 If n is a fixed point, then n^2 belongs to A052383.
%C A288538 The first fixed points are: 3, 6, 7, 8, 15, 20, 23, 24, 25, 26, 27, 28, 45, 47, 60, 64, 65, 66, 67, 68, 75, 76, 77, 78, ...
%H A288538 Rémy Sigrist, <a href="/A288538/b288538.txt">Table of n, a(n) for n = 1..10000</a>
%H A288538 Rémy Sigrist, <a href="/A288538/a288538.gp.txt">PARI program for A288538</a>
%H A288538 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%H A288538 Rémy Sigrist, <a href="/A288538/a288538.png">Logarithmic scatterplot of the first 10000 terms of n * a(n)</a>
%e A288538 The first terms, alongside n * a(n), are:
%e A288538 n       a(n)    n * a(n)
%e A288538 --      ----    --------
%e A288538 1       2       2
%e A288538 2       1       2
%e A288538 3       3       9
%e A288538 4       5       20
%e A288538 5       4       20
%e A288538 6       6       36
%e A288538 7       7       49
%e A288538 8       8       64
%e A288538 9       10      90
%e A288538 10      9       90
%e A288538 11      19      209
%e A288538 12      17      204
%e A288538 13      16      208
%e A288538 14      18      252
%e A288538 15      15      225
%e A288538 16      13      208
%e A288538 17      12      204
%e A288538 18      14      252
%e A288538 19      11      209
%e A288538 20      20      400
%Y A288538 Cf. A004290, A052383.
%K A288538 nonn,base
%O A288538 1,1
%A A288538 _Rémy Sigrist_, Jun 24 2017