cp's OEIS Frontend

A287928 Lexicographically earliest sequence of distinct positive terms such that, if digsum(a(i)) = digsum(a(j)), then either i = j or digsum(a(i+1)) != digsum(a(j+1)) (where digsum is the digital sum, A007953).

%I A287928 #19 Jun 04 2017 16:37:09
%S A287928 1,2,3,4,5,6,7,8,9,10,12,11,13,15,14,16,18,17,19,20,23,21,24,22,25,28,
%T A287928 26,29,27,30,32,31,35,33,36,34,38,37,39,40,45,41,44,43,42,46,47,48,49,
%U A287928 50,54,51,53,57,52,58,55,59,56,60,65,61,66,62,67,63,64
%N A287928 Lexicographically earliest sequence of distinct positive terms such that, if digsum(a(i)) = digsum(a(j)), then either i = j or digsum(a(i+1)) != digsum(a(j+1)) (where digsum is the digital sum, A007953).
%C A287928 This sequence is a permutation of the natural numbers, with inverse A287929.
%C A287928 More generally, if g is a function over the natural numbers with infinitely many distinct values, then there is a lexicographically earliest sequence of distinct positive terms, say f_g, such that, if g(f_g(i)) = g(f_g(j)), then either i = j or g(f_g(i+1)) != g(f_g(j+1)), and f_g is a permutation of the natural numbers:
%C A287928 - in particular, f_A007953 = a,
%C A287928 - and f_tau = A175500 (where tau = A000005),
%C A287928 - if g is injective then f_g = A000027.
%C A287928 Among the first 250000 terms, we have the following fixed points: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 13, 16, 19, 20, 25, 30, 39, 40, 46, 47, 48, 49, 50, 53, 60, 70, 76, 79, 80, 88, 89, 90, 92, 99, 100, 108, 111, 126, 193
%C A287928 , 675.
%H A287928 Rémy Sigrist, <a href="/A287928/b287928.txt">Table of n, a(n) for n = 1..10000</a>
%H A287928 Rémy Sigrist, <a href="/A287928/a287928.gp.txt">PARI program for A287928</a>
%H A287928 Rémy Sigrist, <a href="/A287928/a287928.png">Logarithmic scatterplot of the first 250000 terms</a>
%H A287928 Rémy Sigrist, <a href="/A287928/a287928.pdf">Illustration of the first terms</a>
%H A287928 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A287928 For n = 1..9, a(n) = n satisfies the definition, and digsum(a(n)) = n.
%e A287928 Also a(10) = 10 satisfies the definition, and digsum(a(10)) = 1.
%e A287928 As digsum(a(10)) = digsum(a(1)), digsum(a(11)) != digsum(a(2)).
%e A287928 a(11) = 12 satisfies the definition.
%Y A287928 Cf. A000005, A000027, A007953, A175500, A287929.
%K A287928 nonn,base
%O A287928 1,2
%A A287928 _Rémy Sigrist_, Jun 03 2017