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A368782 Comma transform of A366487.

%I A368782 #19 Jan 05 2024 17:22:01
%S A368782 12,35,94,15,16,28,31,34,37,41,45,55,55,55,55,61,67,74,71,89,98,97,18,
%T A368782 19,11,11,12,13,14,15,16,17,18,19,11,11,12,13,14,15,16,17,18,22,22,24,
%U A368782 26,28,22,22,24,26,28,22,22,24,26,28,22,22,24,26,28,22,22
%N A368782 Comma transform of A366487.
%C A368782 See A367360 for further information.
%C A368782 Let the comma sequence A121805 be known as S or C0.
%C A368782 A366487, the first differences of A121805, is the same as the comma transform of A121805; call it C1.
%C A368782 This sequence is C2 = C(C(S)), the comma transform C iterated twice.
%C A368782 C4 = C2, C5 = C2, ... once the first term (and the last term if the sequence is finite) are removed from the lower iterates of C.
%C A368782 Theorem: C^{i+2}(S) = C^i(S) for i>=2 in general and for i>=0 when all terms of S have two digits and no least significant digit is zero. See link for proof.
%C A368782 Remark. The lexicographically earliest sequence S with C(S) = S is A010850, all 11's.
%C A368782 The sequence contains 2137451 terms, with a(2137451) = 96. The next term does not exist.
%H A368782 Michael S. Branicky, <a href="/A368782/b368782.txt">Table of n, a(n) for n = 1..20000</a>
%H A368782 Michael S. Branicky, <a href="https://docs.google.com/document/d/1PXgz1eGBaUWoy1MlT0hhIkkZoLfFWAfI2TEIdsaA0c4/edit?usp=sharing">Comma Comma Proof</a>
%o A368782 (Python)
%o A368782 from itertools import islice, pairwise
%o A368782 def S(): # generator of comma sequence
%o A368782     an = 1
%o A368782     while True:
%o A368782         yield an
%o A368782         an += 10*(an%10)
%o A368782         children = [an+y for y in range(1, 10) if str(an+y)[0] == str(y)]
%o A368782         if not children: break
%o A368782         an = children[0]
%o A368782 def C(g): # generator of comma transform of sequence passed as a generator
%o A368782     yield from (10*(t%10) + int(str(u)[0]) for t, u in pairwise(g))
%o A368782 def agen(): return C(C(S()))
%o A368782 print(list(islice(agen(), 70))) # _Michael S. Branicky_, Jan 05 2024
%Y A368782 Cf. A010850, A121805, A367360, A366487.
%K A368782 nonn,base
%O A368782 1,1
%A A368782 _Michael S. Branicky_, Jan 05 2024