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A383320 Lexicographically earliest sequence of distinct terms such that replacing each term k with Fibonacci(k) does not change the succession of digits.

%I A383320 #6 Apr 23 2025 10:40:13
%S A383320 0,1,5,43,3,4,9,44,37,2,33,470,140,8,7,332,41,57,81,71,35,24,578,74,
%T A383320 93,86,58,6,61,14,242,47,46,936,9310,13,87,148,48,19,30,12,55,77,36,
%U A383320 270,246,51,68,97,194,4350,50,27,72,31,359,90,22,40,278,505,23
%N A383320 Lexicographically earliest sequence of distinct terms such that replacing each term k with Fibonacci(k) does not change the succession of digits.
%H A383320 Dominic McCarty, <a href="/A383320/b383320.txt">Table of n, a(n) for n = 1..10000</a>
%e A383320 Let b(n) = Fibonacci(a(n))
%e A383320 (a(n)): 0, 1, 5, 43, 3, 4, 9, 44, 37, 2, ...
%e A383320 (b(n)): 0, 1, 5, 433494437,           2, ...
%o A383320 (Python)
%o A383320 from sympy import fibonacci
%o A383320 from itertools import count
%o A383320 a, sa, sb = [0,1,5,43], "01543", "015433494437"
%o A383320 for _ in range(30):
%o A383320     a.append(next(n for k in count(1) if not (n := int(sb[len(sa):len(sa)+k])) in a and not (len(sb) > len(sa) + k and sb[len(sa) + k] == "0")))
%o A383320     sa += str(a[-1]); sb += str(fibonacci(a[-1]))
%o A383320 print(a)
%Y A383320 Cf. A383321 (Fibonacci(a(n))), A038546, A383318, A383322, A302656.
%K A383320 nonn,base
%O A383320 1,3
%A A383320 _Dominic McCarty_, Apr 23 2025