A256658 Rectangular array by antidiagonals: row n consists of numbers k such that F(n+1) is the trace of the minimal alternating Fibonacci representation of k, where F = A000045 (Fibonacci numbers).
1, 9, 2, 14, 15, 3, 17, 23, 24, 5, 22, 28, 37, 39, 8, 27, 36, 45, 60, 63, 13, 30, 44, 58, 73, 97, 102, 21, 35, 49, 71, 94, 118, 157, 165, 34, 43, 57, 79, 115, 152, 191, 254, 267, 55, 48, 70, 92, 128, 186, 246, 309, 411, 432, 89, 51, 78, 113, 149, 207, 301
Offset: 1
Examples
Northwest corner: 1 9 14 17 22 27 30 35 43 2 15 23 28 36 44 49 57 70 3 24 37 45 58 71 79 92 113 5 39 69 73 94 115 128 149 183 8 63 97 118 152 186 207 241 296 13 102 157 191 246 301 335 390 479
Programs
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Mathematica
b[n_] = Fibonacci[n]; bb = Table[b[n], {n, 1, 70}]; h[0] = {1}; h[n_] := Join[h[n - 1], Table[b[n + 2], {k, 1, b[n]}]]; g = h[18]; r[0] = {0}; r[n_] := If[MemberQ[bb, n], {n}, Join[{g[[n]]}, -r[g[[n]] - n]]]; t = Table[Last[r[n]], {n, 0, 1000}]; (* A256656 *) TableForm[Table[Flatten[-1 + Position[t, b[n]]], {n, 2, 8}]] (* A256658 *) TableForm[Table[Flatten[-1 + Position[t, -b[n]]], {n, 2, 8}]] (* A256659 *)
Comments