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A369798 S is a "boomerang sequence": multiply each digit d of S by the number to which d belongs: the sequence S remains identical to itself if we follow each multiplication with a comma.

%I A369798 #30 Feb 05 2024 10:49:41
%S A369798 0,1,12,24,48,96,192,384,864,576,192,1728,384,1152,3072,1536,6912,
%T A369798 5184,3456,2880,4032,3456,192,1728,384,1728,12096,3456,13824,1152,
%U A369798 3072,1536,1152,1152,5760,2304,9216,0,21504,6144,1536,7680,4608,9216,41472,62208,6912,13824,25920,5184,41472,20736,10368,13824
%N A369798 S is a "boomerang sequence": multiply each digit d of S by the number to which d belongs: the sequence S remains identical to itself if we follow each multiplication with a comma.
%C A369798 S is the lexicographycally earliest nontrivial sequence of nonnegative integers with this property (if we try for a(3) the integers 1, 10 or 11, we respectively get these trivial sequences):
%C A369798 S = 1, 1, 1, 1, 1, 1, 1, ...
%C A369798 S = 1, 10, 0, 0, 0, 0, 0, ...
%C A369798 S = 1, 11, 1, 1, 1, 1, 1, ...
%H A369798 Eric Angelini and Jean-Marc Falcoz, <a href="https://cinquantesignes.blogspot.com/2024/02/boomerang-sequences.html">Boomerang sequences</a>, Personal blog, Feb 1st 2024.
%e A369798 a(1) = 0, which multiplied by 0 gives 0
%e A369798 a(2) = 1, which multiplied by 1 gives 1
%e A369798 a(3) = 12
%e A369798      1st digit is 1, which multiplied by 12 gives 12
%e A369798      2nd digit is 2, which multiplied by 12 gives 24
%e A369798 a(4) = 24
%e A369798      1st digit is 2, which multiplied by 24 gives 48
%e A369798      2nd digit is 4, which multiplied by 24 gives 96
%e A369798 a(5) = 48
%e A369798      1st digit is 4, which multiplied by 48 gives 192
%e A369798      2nd digit is 8, which multiplied by 48 gives 384
%e A369798 a(6) = 96
%e A369798      1st digit is 9, which multiplied by 96 gives 864
%e A369798      2nd digit is 6, which multiplied by 96 gives 576
%e A369798 Etc. We see that the above last column reproduces S.
%t A369798 Join[{0,1},Nest[Flatten[IntegerDigits@#*#]&,{12},5]] (* _Giorgos Kalogeropoulos_, Feb 01 2024 *)
%o A369798 (Python)
%o A369798 from itertools import islice
%o A369798 from collections import deque
%o A369798 def agen(): # generator of terms
%o A369798     S = deque([24])
%o A369798     yield from [0, 1, 12]
%o A369798     while True:
%o A369798         an = S.popleft()
%o A369798         yield an
%o A369798         S.extend(an*d for d in map(int, str(an)))
%o A369798 print(list(islice(agen(), 54))) # _Michael S. Branicky_, Feb 01 2024
%Y A369798 Cf. A369603, A369604, A369823, A369824.
%K A369798 base,nonn
%O A369798 1,3
%A A369798 _Eric Angelini_ and _Jean-Marc Falcoz_, Feb 01 2024