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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
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.
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
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Jun 03 2017
STATUS
approved