A345471 a(0) = a(1) = 1, a(n) is the smallest positive integer m >= a(n-1) + a(n-2) such that gcd(a(k),m) = 1 for all 1 < k <= n - 1.
1, 1, 2, 3, 5, 11, 17, 29, 47, 79, 127, 211, 343, 557, 907, 1469, 2377, 3847, 6229, 10079, 16319, 26399, 42719, 69119, 111841, 180967, 292811, 473779, 766607, 1240387, 2006999, 3247393, 5254397, 8501791, 13756189, 22258001, 36014191, 58272197, 94286389, 152558587
Offset: 0
Keywords
Examples
a(5) = 11 because 11 is the smallest number greater than or equal to a(3) + a(4) = 5 + 3 = 8 which is coprime to all previous terms of the sequence.
Programs
-
Mathematica
a[0] = a[1] = 1; a[n_] := a[n] = Module[{k = a[n - 1] + a[n - 2]}, While[! AllTrue[Range[2, n - 1], CoprimeQ[a[#], k] &], k++]; k]; Array[a, 40, 0] (* Amiram Eldar, Jun 20 2021 *)
Comments