A201010 Integers that can be written as the product and/or quotient of Lucas numbers.

1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 14, 16, 18, 19, 21, 22, 23, 24, 27, 28, 29, 31, 32, 33, 36, 38, 41, 42, 44, 46, 47, 48, 49, 54, 56, 57, 58, 62, 63, 64, 66, 69, 72, 76, 77, 81, 82, 84, 87, 88, 92, 93, 94, 96, 98, 99, 107, 108, 112, 114, 116, 121, 123, 124, 126, 128

Offset

1,2

Comments

These numbers do not occur in A178777.

The first 20 terms of this sequence are the same as in A004144 (nonhypotenuse numbers).

Integers of the form A200381(n)/A200381(m) for some m and n.

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Lucas Number

Index entries for Lucas sequences

Example

19 is in the sequence because Lucas(9)/Lucas(0)^2 = 19.

Mathematica

maxTerm = 128; Clear[f]; f[lim_] := f[lim] = (luc = LucasL[Range[0, lim]]; luc = Delete[luc, 2];  last = luc[[-1]]; t = {1}; Do[t2 = luc[[n]]^Range[ Floor[ Log[last] / Log[ luc[[n]] ]]]; s = Select[ Union[ Flatten[ Outer[ Times, t, t2]]], # <= last &]; t = Union[t, s], {n, lim}]; maxIndex = Length[A200381 = t]; Reap[ Do[r = A200381[[n]] / A200381[[m]]; If[IntegerQ[r] && r <= maxTerm, Sow[r]], {n, 1, maxIndex}, {m, 1, maxIndex}]][[2, 1]] // Union); f[5]; f[lim = 10]; While[ Print["lim = ", lim]; f[lim] != f[lim-5], lim = lim+5]; f[lim] (* Jean-François Alcover, Jun 24 2015, after script by T. D. Noe in A200381 *)

Crossrefs

Cf. A000032, A200381, A200995, A201011. Subsequence of A178772. Complement of A201012.

Sequence in context: A343109 A209921 A268377 * A004144 A356930 A124391

Adjacent sequences: A201007 A201008 A201009 * A201011 A201012 A201013

Keyword

nice,nonn

Author

Arkadiusz Wesolowski, Jan 08 2013

Status

approved