A395853 - OEIS

%I #22 Jun 15 2026 17:48:22

%S 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,

%T 38,43,46,55,56,59,64,65,66,67,69,72,77,80,85,89,90,93,98,114,119,144,

%U 145,148,153,169,170,171,172,174,177,182,190,203,208,224,233,234,237,242,258,297,313,377

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

%H Robert Israel, <a href="/A395853/b395853.txt">Table of n, a(n) for n = 1..10000</a>

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

%p N:= 10^6: # for terms <= N

%p r:= ceil(log[(1+sqrt(5))/2](sqrt(5)*N)):

%p Fibs:= select(`<=`,[seq(combinat:-fibonacci(i),i=0..r)],N):

%p Fibsq:= select(`<=`,map(t -> t^2, Fibs), N):

%p sort(convert(select(`<=`,{seq(seq(a+b,a=Fibs),b=Fibsq)}, N),list));

%Y Complement of A354626. Cf. A000045, A007598.

%K nonn

%O 1,3

%A _Robert Israel_, Jun 10 2026