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A333028 Array consisting of the primitive rows of the Wythoff array (A035513), read by antidiagonals.

%I A333028 #10 Apr 13 2020 01:39:58
%S A333028 1,2,4,3,7,14,5,11,23,17,8,18,37,28,19,13,29,60,45,31,25,21,47,97,73,
%T A333028 50,41,27,34,76,157,118,81,66,44,30,55,123,254,191,131,107,71,49,35,
%U A333028 89,199,411,309,212,173,115,79,57,43,144,322,665,500,343,280
%N A333028 Array consisting of the primitive rows of the Wythoff array (A035513), read by antidiagonals.
%C A333028 In a row of the Wythoff array, either every two consecutive terms are relatively prime or else no two consecutive terms are relatively prime. In the first case, we call the row primitive; otherwise, the row is an integer multiple of a tail of a preceding row. The primitive rows are interspersed, in the sense that if h < k then the numbers in row k are interspersed, in magnitude, among numbers in row h. In each row, every pair of consecutive numbers is a Wythoff pair of relatively prime numbers. The array includes every prime.
%e A333028 Northwest corner:
%e A333028    1   2   3    5    8   13  21    34
%e A333028    4   7  11   18   29   47  76   123
%e A333028   14  23  37   60   97  157  254  411
%e A333028   17  28  45   73  118  191  309  500
%e A333028   19  31  50   81  131  212  343  555
%e A333028   25  41  66  107  173  280  453  733
%e A333028   27  44  71  115  186  301  487  788
%e A333028   30  49  79  128  207  335  542  877
%t A333028 W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k];
%t A333028 t = Table[GCD[W[n, 1], W[n, 2]], {n, 1, 160}]
%t A333028 u = Flatten[Position[t, 1]]; v[n_, k_] := W[u[[n]], k];
%t A333028 TableForm[Table[v[n, k], {n, 1, 30}, {k, 1, 8}]] (* A333028 array *)
%t A333028 Table[v[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten  (* A333028 sequence *)
%Y A333028 Cf. A000045, A000032, A332937, A332938, A333029, A333086.
%K A333028 nonn,tabl,easy
%O A333028 1,2
%A A333028 _Clark Kimberling_, Mar 10 2020