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%I #8 Jun 04 2023 23:50:37
%S 1,1,1,2,2,1,7,8,6,2,8,6,10,17,2,21,23,24,26,11,7,12,20,1,6,39,40,10,
%T 26,17,49,8,53,21,14,36,6,63,40,10,69,27,7,46,76,2,81,33,54,88,1,92,
%U 14,23,38,64,66,42,27,74,18,80,84,53,54,90,94,59,60,24
%N a(n) = number of the row of the Wythoff array (A035513) that includes prime(n).
%C Conjecture: every primitive row number, as defined in A332938, occurs infinitely many times in this sequence.
%F 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 m such that prime(n) = p(m,k) for some k.
%e The 10th prime is 29, which occurs in row 7, so a(10) = 2.
%t W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k];
%t t = Table[W[n, k], {n, 100}, {k, 1, 20}];
%t a[n_] := Select[Range[100], MemberQ[t[[#]], Prime[n]] &]
%t Flatten[Table[a[n], {n, 1, 100}]]
%Y Cf. A000040, A035513, A332938, A360378, A360379, A360380.
%K nonn,easy
%O 1,4
%A _Clark Kimberling_, Feb 04 2023
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