Irregular table of conjectured Lucas numbers with exactly n bits set in binary.
1, 2, 4, 3, 18, 7, 11, 76, 322, 521, 29, 47, 199, 1364, 9349, 123, 843, 5778, 103682, 2207, 271443, 3571, 15127, 39603, 167761, 24476, 439204, 1860498, 64079, 1149851, 7881196, 12752043, 370248451, 17393796001, 54018521, 4870847, 10749957122, 599074578, 710647
1
T. D. Noe, Plot of the first 1000 rows
T. D. Noe, Terms in the first 1000 rows
The irregular table is conjectured to begin
{1, 2, 4},
{3, 18},
{7, 11, 76, 322, 521},
{29},
{47, 199, 1364, 9349},
{123, 843, 5778, 103682},
{2207, 271443}
(Mma) f = LucasL[Range[0, 200]]; t = Table[Sort[Select[f, Total[IntegerDigits[#, 2]] == n &]], {n, 20}]; Flatten[t]
Cf. A000032 (Lucas numbers).
Cf. S000057 (similar, but Fibonacci numbers), S000058 (Lucas numbers in binary).
nonn,tabf
T. D. Noe, May 19 2014