A303217 A(n,k) is the n-th index of a Fibonacci number with exactly k distinct prime factors; square array A(n,k), n>=1, k>=1, read by antidiagonals.
3, 8, 4, 15, 9, 5, 20, 16, 10, 6, 30, 24, 18, 12, 7, 40, 36, 27, 21, 14, 11, 70, 48, 42, 28, 33, 19, 13, 60, 81, 54, 44, 32, 35, 22, 17, 80, 72, 104, 56, 45, 52, 37, 25, 23, 90, 84, 110, 105, 64, 50, 55, 38, 26, 29, 140, 126, 88, 112, 136, 78, 57, 74, 39, 31, 43
Offset: 1
Examples
Square array A(n,k) begins: 3, 8, 15, 20, 30, 40, 70, 60, 80, 90, ... 4, 9, 16, 24, 36, 48, 81, 72, 84, 126, ... 5, 10, 18, 27, 42, 54, 104, 110, 88, 165, ... 6, 12, 21, 28, 44, 56, 105, 112, 96, 256, ... 7, 14, 33, 32, 45, 64, 136, 114, 100, 258, ... 11, 19, 35, 52, 50, 78, 148, 128, 108, 266, ... 13, 22, 37, 55, 57, 92, 152, 130, 132, 296, ... 17, 25, 38, 74, 63, 95, 164, 135, 138, 304, ... 23, 26, 39, 77, 66, 99, 182, 147, 156, 322, ... 29, 31, 46, 85, 68, 102, 186, 154, 184, 369, ...
Links
- Alois P. Heinz, Antidiagonals n = 1..18, flattened
Crossrefs
Programs
-
Maple
F:= combinat[fibonacci]: with(numtheory): A:= proc() local h, p, q; p, q:= proc() [] end, 2; proc(n, k) while nops(p(k)) -
Mathematica
nmax = 12; maxIndex = 200; nu[n_] := nu[n] = PrimeNu[Fibonacci[n]]; col[k_] := Select[Range[maxIndex], nu[#] == k&]; T = Array[col, nmax]; A[n_, k_] := T[[k, n]]; Table[A[n-k+1, k], {n, 1, nmax}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Jan 04 2020 *)