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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
OFFSET
1,1
LINKS
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
KEYWORD
nonn,tabl
AUTHOR
Alois P. Heinz, Apr 19 2018
STATUS
approved