

A362551


a(0)=0. For each digit d in the sequence, append the smallest unused integer such that its last digit equals d.


2



0, 10, 1, 20, 11, 2, 30, 21, 31, 12, 3, 40, 22, 41, 13, 51, 61, 32, 23, 4, 50, 42, 52, 14, 71, 81, 33, 5, 91, 6, 101, 43, 62, 72, 53, 24, 15, 60, 34, 82, 25, 92, 111, 44, 7, 121, 8, 131, 63, 73, 35, 9, 141, 16, 151, 70, 161, 54, 83, 26, 102, 17, 112, 45, 93
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OFFSET

0,2


COMMENTS

This sequence is a permutation of the nonnegative integers.


LINKS



EXAMPLE

a(0) = 0
a(1) = 10 (d=0 from a(0)=0, smallest integer other than 0 that ends with 0).
a(2) = 1 (d=1 from a(1)=10, smallest integer that ends with a 1).
a(3) = 20 (d=0 from a(1)=10, smallest integer other than 0 and 10 that ends with 0).
a(4) = 11 (d=1 from a(2)=1, smallest integer other than 1 that ends with 1).
a(5) = 2 (d=2 from a(3)=20, smallest integer that ends with 2).
a(6) = 30 (d=0 from a(3)=20, smallest integer other than 0, 10, and 20 that ends with 0).


PROG

(Python)
from itertools import count, islice
def agen(): # generator of terms
s, lastd = "0", [(k for k in count(i, 10)) for i in range(10)]
for n in count(0):
an = next(lastd[int(s[0])])
s = s[1:] + str(an)
yield an


CROSSREFS



KEYWORD

nonn,base,easy


AUTHOR



STATUS

approved



