A345020 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.

1, 1, 2, 3, 5, 7, 11, 17, 23, 37, 59, 89, 139, 227, 361, 587, 947, 1531, 2477, 4007, 6481, 10487, 16963, 27449, 44393, 71837, 116227, 188063, 304289, 492343, 796627, 1288967, 2085593, 3374557, 5460139, 8834689, 14294827, 23129507, 37424333, 60553837, 97978169

Offset: 0

Author

Amrit Awasthi, Jun 05 2021

Keywords

• nonn

Comments

First differs from A055500 at a(14).

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..4781

Crossrefs

Cf. A055500.

Programs

Maple

A[0]:= 1:
A[1]:= 1: P:= 1:
for n from 2 to 100 do
  for k from A[n-2]+A[n-1] by -1 do
    if igcd(k,P) = 1 then break fi
  od;
  A[n]:= k;
  P:= P*k;
od:
convert(A,list); # Robert Israel, Oct 23 2024

Mathematica

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 *)