

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).


2



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, 26, 29, 27, 30, 32, 31, 35, 33, 36, 34, 38, 37, 39, 40, 45, 41, 44, 43, 42, 46, 47, 48, 49, 50, 54, 51, 53, 57, 52, 58, 55, 59, 56, 60, 65, 61, 66, 62, 67, 63, 64
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

This sequence is a permutation of the natural numbers, with inverse A287929.
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:
 in particular, f_A007953 = a,
 and f_tau = A175500 (where tau = A000005),
 if g is injective then f_g = A000027.
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
, 675.


LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A287928
Rémy Sigrist, Logarithmic scatterplot of the first 250000 terms
Rémy Sigrist, Illustration of the first terms
Index entries for sequences that are permutations of the natural numbers


EXAMPLE

For n = 1..9, a(n) = n satisfies the definition, and digsum(a(n)) = n.
Also a(10) = 10 satisfies the definition, and digsum(a(10)) = 1.
As digsum(a(10)) = digsum(a(1)), digsum(a(11)) != digsum(a(2)).
a(11) = 12 satisfies the definition.


CROSSREFS

Cf. A000005, A000027, A007953, A175500, A287929.
Sequence in context: A209862 A209861 A287929 * A085516 A276444 A276443
Adjacent sequences: A287925 A287926 A287927 * A287929 A287930 A287931


KEYWORD

nonn,base


AUTHOR

Rémy Sigrist, Jun 03 2017


STATUS

approved



