cp's OEIS Frontend

A358359 a(n) = number of occurrences of n in A128440; i.e., as a number [k*r^m], where r = golden ratio = (1+sqrt(5))/2, k and m are positive integers, and [ ] = floor.

%I A358359 #7 Nov 13 2022 08:38:29
%S A358359 1,1,1,2,1,2,1,2,1,1,2,2,2,1,1,2,2,1,1,2,2,2,1,1,2,1,2,1,3,1,1,1,3,2,
%T A358359 2,1,1,2,1,1,2,2,1,2,1,3,2,1,1,2,1,1,2,2,3,1,1,2,2,1,2,1,2,1,1,2,2,2,
%U A358359 1,1,2,2,1,1,2,3,2,1,1,2,1,2,1,2,1,1
%N A358359 a(n) = number of occurrences of n in A128440; i.e., as a number [k*r^m], where r = golden ratio = (1+sqrt(5))/2, k and m are positive integers, and [ ] = floor.
%C A358359 Conjecture: every positive integers occurs infinitely many times.
%t A358359 r = (1 + Sqrt[5])/2; f[n_] := Fibonacci[n]; nr = 300; nc = 200;
%t A358359 t[n_, k_] := k*f[n - 1] + Floor[k*r*f[n]];  (* A128440 *)
%t A358359 u = Sort[Flatten[Table[t[k, n], {k, 1, nr}, {n, 1, nc}]]];
%t A358359 Table[Count[u, n], {n, 1, nr}]
%Y A358359 Cf. A128440.
%K A358359 nonn
%O A358359 1,4
%A A358359 _Clark Kimberling_, Nov 11 2022