A362551 a(0)=0. For each digit d in the sequence, append the smallest unused integer such that its last digit equals d.

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

Offset

0,2

Comments

This sequence is a permutation of the nonnegative integers.

Links

Gavin Lupo, Table of n, a(n) for n = 0..10000

Gavin Lupo, Image of the first 10000 terms.

Index entries for sequences that are permutations of the nonnegative integers

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
print(list(islice(agen(), 65))) # Michael S. Branicky, Apr 25 2023

Crossrefs

Cf. A106001, A362371.

Sequence in context: A317054 A292690 A362371 * A036188 A013617 A243002

Adjacent sequences: A362548 A362549 A362550 * A362552 A362553 A362554

Keyword

nonn,base,easy

Author

Gavin Lupo, Apr 24 2023

Status

approved