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%I #16 Jun 07 2021 10:40:20
%S 1,1,2,3,5,7,11,17,23,37,59,89,139,227,361,587,947,1531,2477,4007,
%T 6481,10487,16963,27449,44393,71837,116227,188063,304289,492343,
%U 796627,1288967,2085593,3374557,5460139,8834689,14294827,23129507,37424333,60553837,97978169
%N a(0) = a(1) = 1, a(n) = largest natural number m <= a(n-1) + a(n-2) where gcd(m,a(k)) = 1 for all 1 < k <= n-1.
%C First differs from A055500 at a(14).
%e a(5) = 7 because 7 is the largest number less than or equal to a(4) + a(3) = 8 which is coprime to all the previous terms of sequence.
%t a[0] = a[1] = 1; a[n_] := a[n] = Module[{k = a[n - 1] + a[n - 2]}, While[! AllTrue[Range[2, n - 2], CoprimeQ[a[#], k] &], k--]; k]; Array[a, 50, 0] (* _Amiram Eldar_, Jun 05 2021 *)
%Y Cf. A055500.
%K nonn
%O 0,3
%A _Amrit Awasthi_, Jun 05 2021
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