A379835 Number of 1's in binary expansion of Lucas(n).

1, 1, 2, 1, 3, 3, 2, 4, 5, 3, 6, 5, 3, 3, 6, 5, 7, 9, 6, 5, 9, 10, 9, 11, 6, 9, 7, 10, 15, 11, 10, 15, 13, 11, 11, 15, 15, 12, 15, 17, 15, 11, 14, 15, 20, 15, 18, 17, 13, 11, 22, 20, 23, 23, 19, 22, 22, 22, 28, 25, 23, 19, 25, 27, 27, 24, 26, 25, 23, 27, 23, 27

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Formula

a(n) = A000120(A000032(n)).

Example

a(10) = 6 because Lucas(10) = 123 is 1111011_2, which has 6 one bits.

Maple

f:= n -> convert(convert(combinat:-fibonacci(n+1) + combinat:-fibonacci(n-1), base, 2), `+`):
map(f, [$0..100]); # Robert Israel, May 15 2026

Mathematica

Table[DigitCount[LucasL[n], 2][[1]], {n, 0, 200}]

Prog

(Magma) [&+Intseq(Lucas(n), 2): n in [0..100]];

Crossrefs

Cf. A000032, A000120, A011373.

Sequence in context: A006642 A376239 A332435 * A361744 A324751 A210595

Adjacent sequences: A379832 A379833 A379834 * A379836 A379837 A379838

Keyword

nonn,base

Author

Vincenzo Librandi, Jan 05 2025

Status

approved