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A333028 Array consisting of the primitive rows of the Wythoff array (A035513), read by antidiagonals. 4
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, 50, 41, 27, 34, 76, 157, 118, 81, 66, 44, 30, 55, 123, 254, 191, 131, 107, 71, 49, 35, 89, 199, 411, 309, 212, 173, 115, 79, 57, 43, 144, 322, 665, 500, 343, 280 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..61.

EXAMPLE

Northwest corner:

   1   2   3    5    8   13  21    34

   4   7  11   18   29   47  76   123

  14  23  37   60   97  157  254  411

  17  28  45   73  118  191  309  500

  19  31  50   81  131  212  343  555

  25  41  66  107  173  280  453  733

  27  44  71  115  186  301  487  788

  30  49  79  128  207  335  542  877

MATHEMATICA

W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k];

t = Table[GCD[W[n, 1], W[n, 2]], {n, 1, 160}]

u = Flatten[Position[t, 1]]; v[n_, k_] := W[u[[n]], k];

TableForm[Table[v[n, k], {n, 1, 30}, {k, 1, 8}]] (* A333028 array *)

Table[v[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten  (* A333028 sequence *)

CROSSREFS

Cf. A000045, A000032, A332937, A332938, A333029, A333086.

Sequence in context: A138612 A246680 A294244 * A296449 A309201 A253792

Adjacent sequences:  A333025 A333026 A333027 * A333029 A333030 A333031

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, Mar 10 2020

STATUS

approved

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Last modified November 29 23:37 EST 2020. Contains 338780 sequences. (Running on oeis4.)