A395853 Numbers that can be written as the sum of a Fibonacci number and the square of a Fibonacci number.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 17, 21, 22, 25, 26, 27, 28, 30, 33, 34, 35, 38, 43, 46, 55, 56, 59, 64, 65, 66, 67, 69, 72, 77, 80, 85, 89, 90, 93, 98, 114, 119, 144, 145, 148, 153, 169, 170, 171, 172, 174, 177, 182, 190, 203, 208, 224, 233, 234, 237, 242, 258, 297, 313, 377

Offset

1,3

Links

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

Example

a(8) = 7 is a term because 7 = 3 + 2^2 where 3 = A000045(4) and 2 = A000045(3) are Fibonacci numbers.

Maple

N:= 10^6: # for terms <= N
r:= ceil(log[(1+sqrt(5))/2](sqrt(5)*N)):
Fibs:= select(`<=`, [seq(combinat:-fibonacci(i), i=0..r)], N):
Fibsq:= select(`<=`, map(t -> t^2, Fibs), N):
sort(convert(select(`<=`, {seq(seq(a+b, a=Fibs), b=Fibsq)}, N), list));

Crossrefs

Complement of A354626. Cf. A000045, A007598.

Sequence in context: A302140 A039698 A377914 * A347620 A078107 A072089

Adjacent sequences: A395850 A395851 A395852 * A395854 A395855 A395856

Keyword

nonn

Author

Robert Israel, Jun 10 2026

Status

approved