A354626 Numbers that can't be written as the sum of a Fibonacci number and the square of a Fibonacci number.

15, 16, 18, 19, 20, 23, 24, 29, 31, 32, 36, 37, 39, 40, 41, 42, 44, 45, 47, 48, 49, 50, 51, 52, 53, 54, 57, 58, 60, 61, 62, 63, 68, 70, 71, 73, 74, 75, 76, 78, 79, 81, 82, 83, 84, 86, 87, 88, 91, 92, 94, 95, 96, 97, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 115

Offset

1,1

Links

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

Formula

Numbers k such that the coefficient of x^k in the product (Sum_{i>=0} x^Fibonacci(i)) * (Sum_{j>=0} x^(Fibonacci(j)^2)) is 0.

Example

16 is a term since there does not exist any pair of integers i,j >= 0 such that Fibonacci(i) + Fibonacci(j)^2 = 16.

Maple

N:= 1000: # 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):
S:= select(`<=`, {seq(seq(a+b, a=Fibs), b=Fibsq)}, N):
sort(convert({$0 .. N} minus S, list)); # Robert Israel, Jun 11 2026

Crossrefs

Cf. A000045, A007598, A059727. Complement of A395853.

Sequence in context: A358043 A090461 A281879 * A114841 A031168 A108856

Adjacent sequences: A354623 A354624 A354625 * A354627 A354628 A354629

Keyword

nonn,changed

Author

Angad Singh, Jul 09 2022

Status

approved