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A369603 S is a "boomerang sequence": adding 9 to each digit of S and following the result with a comma leaves S unchanged.

%I A369603 #18 Feb 12 2024 08:36:12
%S A369603 10,9,18,10,17,10,9,10,16,10,9,18,10,9,10,15,10,9,18,10,17,10,9,18,10,
%T A369603 9,10,14,10,9,18,10,17,10,9,10,16,10,9,18,10,17,10,9,18,10,9,10,13,10,
%U A369603 9,18,10,17,10,9,10,16,10,9,18,10,9,10,15,10,9,18,10,17,10,9,10,16,10,9,18,10,17,10,9,18,10,9
%N A369603 S is a "boomerang sequence": adding 9 to each digit of S and following the result with a comma leaves S unchanged.
%C A369603 Lexicographically earliest sequence starting with a(1) = 10.
%C A369603 The only integers that appear in the sequence are 9, 10, 11, 12, 13, 14, 15, 16, 17 and 18.
%C A369603 Is this (apart from the first term) the same as A103700? - _R. J. Mathar_, Feb 12 2024
%H A369603 Éric Angelini and Giorgos Kalogeropoulos, <a href="https://cinquantesignes.blogspot.com/2024/01/the-same-sequence-but-differently.html">The same sequence but differently</a>, personal blog, Jan 24th 2024.
%e A369603 Adding 9 to 1 (the 1st digit of 10) gives 10
%e A369603 Adding 9 to 0 (the 2nd digit of 10) gives 9
%e A369603 Adding 9 to 9 (the only digit of 9) gives 18
%e A369603 Adding 9 to 1 (the 1st digit of 18) gives 10
%e A369603 Adding 9 to 8 (the 2nd digit of 18) gives 17, etc.
%e A369603 We see that the last column above is the sequence S itself.
%t A369603 a[1]=10;a[n_]:=a[n]=Flatten[IntegerDigits/@Array[a,n-1]][[n]]+9;Array[a,100]
%o A369603 (Python)
%o A369603 from itertools import islice
%o A369603 def agen(): # generator of terms
%o A369603     an, digits = 10, [0]
%o A369603     while True:
%o A369603         yield an
%o A369603         an = 9 + digits.pop(0)
%o A369603         digits += list(map(int, str(an)))
%o A369603 print(list(islice(agen(), 84))) # _Michael S. Branicky_, Jan 27 2024
%Y A369603 Cf. A103700, A369604, A369798, A369823, A369824.
%K A369603 base,nonn
%O A369603 1,1
%A A369603 _Eric Angelini_ and _Giorgos Kalogeropoulos_, Jan 27 2024