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Lexicographically earliest sequence of distinct positive integers with no finite subset summing to a positive Fibonacci number.
5

%I #8 May 18 2022 10:04:54

%S 4,6,10,12,19,25,40,62,110,178,288,466,576,644,754,1974,2152,2262,

%T 3948,8362,11556,15504,35422,43784,48342,66286,150050,198392,209948,

%U 467861,896352,1357215,2191229,4389456,8351641,11405774,18454930,29860704,48315634

%N Lexicographically earliest sequence of distinct positive integers with no finite subset summing to a positive Fibonacci number.

%C The sequence is well defined:

%C - a(1) = 4,

%C - for n > 0, let k be such that A000045(k) + 1 + a(1) + ... + a(n) < A000045(k+1),

%C - then a(n+1) <= A000045(k) + 1.

%H Rémy Sigrist, <a href="/A353966/a353966.txt">C++ program</a>

%o (C++) See Links section.

%Y See A353889 for similar sequences.

%Y Cf. A000045, A353967, A353968.

%K nonn

%O 1,1

%A _Rémy Sigrist_, May 12 2022