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).

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

Offset: 1

Author

Rémy Sigrist, Jun 03 2017

Keywords

• nonn
• base

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.

Examples

			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.
		

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

Crossrefs

Cf. A000005, A000027, A007953, A175500, A287929.