A360227 The succession of the digits of the sequence is the same when each term is multiplied by 11.

1, 11, 2, 12, 21, 3, 22, 31, 33, 24, 23, 4, 13, 6, 32, 64, 25, 34, 41, 43, 66, 35, 270, 42, 7, 5, 37, 44, 51, 47, 372, 63, 8, 52, 9, 70, 46, 27, 75, 540, 74, 84, 56, 15, 17, 40, 92, 69, 38, 85, 72, 99, 770, 50, 62, 97, 82, 55, 940, 81, 49, 246, 16, 165, 18, 7440

Offset

1,2

Comments

This is the lexicographically earliest sequence of positive distinct terms with this property. A similar sequence could be computed with a(1) = 1 and a(2) = 12 but that sequence would not be the lexicographically earliest one showing the property. If we try the sequence starting with a(1) = 1 and a(2) = 10, we immediately see that no a(3) can extend the sequence (this is due to the digit "0" present in 10).

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

The values of a(n) * 11 begin:
   1 * 11 = 11,
  11 * 11 = 121,
   2 * 11 = 22,
  12 * 11 = 132,
  21 * 11 = 231,
   3 * 11 = 33,
  22 * 11 = 242, etc.
We see that the succession of digits in the first column is the same as the succession of digits in the last column.

Prog

(Python)
from itertools import count, islice
def agen(): # generator of terms
    aset, an, s = {"1", "11"}, 2, "21"
    yield from [1, 11]
    while True:
        i = next(i for i in range(1, len(s)+1) if s[:i] not in aset and (i == len(s) or s[i] != "0"))
        an = int(str(s[:i]))
        s = s[i:] + str(an*11)
        aset.add(str(an))
        yield an
print(list(islice(agen(), 66))) # Michael S. Branicky, Apr 28 2023

Crossrefs

Cf. A362433.

Sequence in context: A323484 A330521 A338191 * A318927 A267320 A303785

Adjacent sequences: A360224 A360225 A360226 * A360228 A360229 A360230

Keyword

base,nonn

Author

Eric Angelini, Apr 20 2023

Extensions

a(36) and beyond from Michael S. Branicky, Apr 28 2023

Status

approved