A396985 Numbers whose Fibonacci-Lucas and Lucas-Fibonacci representations have the same number of terms.

1, 3, 6, 9, 12, 14, 15, 16, 20, 27, 32, 33, 37, 40, 43, 46, 52, 53, 61, 63, 64, 67, 69, 70, 71, 75, 84, 85, 87, 98, 101, 106, 108, 116, 121, 122, 130, 136, 137, 139, 142, 158, 159, 160, 164, 166, 171, 172, 175, 177, 181, 184, 187, 190, 196, 197, 220, 221, 223, 226, 229, 232, 260, 265, 266, 268

Offset

1,2

Comments

Numbers k such that A353655(k) = A353656(k).

Numbers k such that A353657(k) = 0.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 6 is a term because the Fibonacci-Lucas representation 6 = 5 + 1 and the Lucas-Fibonacci representation 6 = 4 + 2 both have length 2.

Maple

Fibs:= [seq(combinat:-fibonacci(i), i=2..30)]:
Lucs:= [1, 3, seq(Fibs[n+1]+Fibs[n-1], n=2..28)]:
f:= proc(n, t) local x, i; uses ListTools;
  x:= n;
  for i from 1 do
    if i::t then x:= x - Fibs[BinaryPlace(Fibs, x+1)]
    else x:= x - Lucs[BinaryPlace(Lucs, x+1)]
    fi;
    if x = 0 then return i fi;
  od
end proc:
select(k -> f(k, odd) = f(k, even), [$1..300]);

Crossrefs

Cf. A353655, A353656, A353657.

Sequence in context: A230215 A120688 A102014 * A337091 A168045 A288522

Adjacent sequences: A396981 A396983 A396984 * A396986 A396987 A396988

Keyword

nonn

Author

Robert Israel, Jun 12 2026

Status

approved