This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A360378 #7 Jun 04 2023 23:50:46 %S A360378 2,3,4,2,3,6,1,1,2,5,2,3,2,1,6,1,1,1,1,3,4,3,2,10,5,1,1,4,2,3,1,5,1,3, %T A360378 4,2,6,1,2,5,1,3,6,2,1,9,1,3,2,1,12,1,5,4,3,1,2,1,2,1,3,4,1,2,1,5,1,2, %U A360378 1,1,2,3,3,1,2,1,1,2,3,3,5,2,2,1,2,3 %N A360378 a(n) = number of the column of the Wythoff array (A035513) that includes prime(n). %C A360378 Conjecture: every positive integer occurs infinitely many times in this sequence. %F A360378 Every prime p has a unique representation p = p(m,k) = F(k+1)*[m*tau] + (m-1)*F(k), where F(h) = A000045(h) = h-th Fibonacci number, [ ] = floor, and tau = (1+sqrt(5))/2 = golden ratio, as in A001622. Here, a(n) is the number k such that prime(n) = p(m,k) for some m. %e A360378 The 10th prime is 29, which occurs in column 5, so a(10) = 5. %t A360378 W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k]; %t A360378 t = Table[W[n, k], {k, 200}, {n, 1, 600}]; %t A360378 a[n_] := Select[Range[200], MemberQ[t[[#]], Prime[n]] &] %t A360378 Flatten[Table[a[n], {n, 1, 100}]] %Y A360378 Cf. A000040, A035513, A332938, A360377, A360379, A360380. %K A360378 nonn,easy %O A360378 1,1 %A A360378 _Clark Kimberling_, Feb 04 2023