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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. 19
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Alois P. Heinz, Antidiagonals n = 1..18, flattened

FORMULA

A000045(A(n,k)) = A303218(n,k).

A001221(A000045(A(n,k))) = k.

EXAMPLE

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, ...

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:= nops(factorset(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

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-Fran├žois Alcover, Jan 04 2020 *)

CROSSREFS

Columns k=2-16 give: A114842, A114841, A114843, A114840, A114839, A114838, A114837, A114836, A114826, A114825, A114824, A114823, A117529, A117551, A117550.

Row n=1 gives: A060320.

Cf. A000045, A001221, A022307, A303215, A303218.

Sequence in context: A225456 A212886 A127438 * A106292 A072247 A051359

Adjacent sequences:  A303214 A303215 A303216 * A303218 A303219 A303220

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Apr 19 2018

STATUS

approved

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Last modified May 31 22:29 EDT 2020. Contains 334756 sequences. (Running on oeis4.)