A360227 - OEIS

%I #26 Apr 29 2023 17:04:39

%S 1,11,2,12,21,3,22,31,33,24,23,4,13,6,32,64,25,34,41,43,66,35,270,42,

%T 7,5,37,44,51,47,372,63,8,52,9,70,46,27,75,540,74,84,56,15,17,40,92,

%U 69,38,85,72,99,770,50,62,97,82,55,940,81,49,246,16,165,18,7440

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

%C 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).

%H Michael S. Branicky, <a href="/A360227/b360227.txt">Table of n, a(n) for n = 1..10000</a>

%e The values of a(n) * 11 begin:

%e    1 * 11 = 11,

%e   11 * 11 = 121,

%e    2 * 11 = 22,

%e   12 * 11 = 132,

%e   21 * 11 = 231,

%e    3 * 11 = 33,

%e   22 * 11 = 242, etc.

%e We see that the succession of digits in the first column is the same as the succession of digits in the last column.

%o (Python)

%o from itertools import count, islice

%o def agen(): # generator of terms

%o     aset, an, s = {"1", "11"}, 2, "21"

%o     yield from [1, 11]

%o     while True:

%o         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"))

%o         an = int(str(s[:i]))

%o         s = s[i:] + str(an*11)

%o         aset.add(str(an))

%o         yield an

%o print(list(islice(agen(), 66))) # _Michael S. Branicky_, Apr 28 2023

%Y Cf. A362433.

%K base,nonn

%O 1,2

%A _Eric Angelini_, Apr 20 2023

%E a(36) and beyond from _Michael S. Branicky_, Apr 28 2023