A303215 A(n,k) is the n-th index of a Fibonacci number with exactly k prime factors (counted with multiplicity); square array A(n,k), n>=1, k>=1, read by antidiagonals.

3, 8, 4, 6, 9, 5, 20, 15, 10, 7, 18, 27, 16, 14, 11, 12, 44, 28, 21, 19, 13, 30, 40, 45, 32, 25, 22, 17, 54, 42, 50, 57, 52, 33, 26, 23, 24, 78, 56, 64, 63, 55, 35, 31, 29, 36, 80, 102, 66, 75, 68, 74, 37, 34, 43, 138, 100, 88, 128, 70, 92, 69, 77, 38, 41, 47

Offset

1,1

Links

Alois P. Heinz, Antidiagonals n = 1..16, flattened

Formula

A000045(A(n,k)) = A303216(n,k).

A001222(A000045(A(n,k))) = k.

Example

Square array A(n,k) begins:
   3,  8,  6, 20, 18,  12,  30,  54,  24,  36, ...
   4,  9, 15, 27, 44,  40,  42,  78,  80, 100, ...
   5, 10, 16, 28, 45,  50,  56, 102,  88, 114, ...
   7, 14, 21, 32, 57,  64,  66, 128, 110, 165, ...
  11, 19, 25, 52, 63,  75,  70, 130, 112, 174, ...
  13, 22, 33, 55, 68,  92,  81, 135, 184, 256, ...
  17, 26, 35, 74, 69,  95, 104, 147, 186, 266, ...
  23, 31, 37, 77, 76,  99, 105, 154, 189, 273, ...
  29, 34, 38, 85, 91, 116, 136, 170, 196, 282, ...
  43, 41, 39, 87, 98, 117, 148, 171, 225, 296, ...

Maple

F:= combinat[fibonacci]: with(numtheory):
A:= proc() local h, p, q; p, q:= proc() [] end, 2;
      proc(n, k)
        while nops(p(k))<n do q:= q+1;
          h:= bigomega(F(q));
          p(h):= [p(h)[], (q)]
        od; p(k)[n]
      end
    end():
seq(seq(A(n, 1+d-n), n=1..d), d=1..12);

Mathematica

A[n_, k_] := Module[{h, p, q = 2}, p[k] = {}; While[Length[p[k]]<n, q++; h = PrimeOmega[Fibonacci[q]]; AppendTo[p[h], q]]; p[k][[n]] ];
Table[A[n, 1+d-n], {d, 1, 12}, {n, 1, d}] // Flatten (* Jean-François Alcover, Apr 30 2018, after Alois P. Heinz *)

Crossrefs

Columns k=1-13 give: A001605, A072381, A114812, A114813, A114814, A114815, A114816, A114817, A114818, A114819, A114820, A114821, A114822.

Row n=1 gives A072396.

Cf. A000045, A001222, A038575, A303216, A303217.

Sequence in context: A103559 A021030 A276682 * A240242 A340782 A010628

Adjacent sequences: A303212 A303213 A303214 * A303216 A303217 A303218

Keyword

nonn,tabl

Author

Alois P. Heinz, Apr 19 2018

Status

approved