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A351631 The numbers that are not doubled in column -1 of the extended Trithoff (tribonacci) array.

%I A351631 #18 Jul 03 2025 23:25:13
%S A351631 0,2,4,6,9,11,13,15,17,19,22,24,26,28,30,33,35,37,39,41,43,46,48,50,
%T A351631 53,55,57,59,61,63,66,68,70,72,74,77,79,81,83,85,87,90,92,94,96,98,
%U A351631 100,103,105,107,109,111,114,116,118,120,122,124,127,129,131,134,136,138,140,142,144,147,149,151
%N A351631 The numbers that are not doubled in column -1 of the extended Trithoff (tribonacci) array.
%C A351631 Excluding zeros, these are the indices of letters b and c in the tribonacci word.
%C A351631 The complement of A003144: the indices of the letter a in the tribonacci word. These numbers are doubled in column -1 in the extended Trithoff array.
%C A351631 Also integers with "even" lazy tribonacci representation A352103, and first column of A385436. - _A.H.M. Smeets_, Jun 29 2025
%H A351631 A.H.M. Smeets, <a href="/A351631/b351631.txt">Table of n, a(n) for n = 1..20000</a>
%o A351631 (Python)
%o A351631 def ToDual_111_Zeck(n):
%o A351631     if n == 0:
%o A351631         return "0"
%o A351631     f0, f1, f2, sf = 1, 0, 0, 0
%o A351631     while n > sf:
%o A351631         f0, f1, f2 = f0+f1+f2, f0, f1
%o A351631         sf += f0
%o A351631     r, s = sf-n, "1"
%o A351631     while f0 > 1:
%o A351631         f0, f1, f2 = f1, f2, f0-f1-f2
%o A351631         r, s = r%f0, s+str(1-r//f0)
%o A351631     return s
%o A351631 n, a = 0, 0
%o A351631 while n < 70:
%o A351631     s = ToDual_111_Zeck(a)
%o A351631     if s[len(s)-1] == "0": # == even
%o A351631         n += 1
%o A351631         print(a, end = ", ")
%o A351631 a += 1 # _A.H.M. Smeets_, Jun 28 2025
%Y A351631 Cf. A000073, A003144, A003145, A003146, A136175, A353083, A353084, A353086, A353090.
%K A351631 nonn
%O A351631 1,2
%A A351631 _Tanya Khovanova_ and PRIMES STEP Senior group, May 04 2022