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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. 17
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 (list; table; graph; refs; listen; history; text; internal format)
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-Fran├žois 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.

Cd. A000045, A001222, A038575, A303216, A303217.

Sequence in context: A103559 A021030 A276682 * A240242 A010628 A225456

Adjacent sequences:  A303212 A303213 A303214 * A303216 A303217 A303218

KEYWORD

nonn,tabl

AUTHOR

Alois P. Heinz, Apr 19 2018

STATUS

approved

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Last modified October 21 11:05 EDT 2019. Contains 328294 sequences. (Running on oeis4.)