A356809 Fibonacci numbers which are not the sum of two squares.

3, 21, 55, 987, 2584, 6765, 17711, 46368, 317811, 832040, 2178309, 5702887, 14930352, 102334155, 267914296, 701408733, 1836311903, 4807526976, 12586269025, 32951280099, 86267571272, 225851433717, 591286729879, 1548008755920, 10610209857723

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..472

Example

F(4) = 3; 3 != x^2 + y^2 as no positive integers x, y >= 0 are the solution of this Diophantine equation.

Mathematica

Select[Fibonacci[Range[65]], SquaresR[2, #] == 0 &] (* Amiram Eldar, Aug 29 2022 *)

Prog

(PARI) is(n)=if(n%4==3, return(1)); my(f=factor(n)); for(i=1, #f~, if(f[i, 1]%4==3 && f[i, 2]%2, return(1))); 0; \\ A022544
lista(nn) = select(is, apply(fibonacci, [1..nn])); \\ Michel Marcus, Sep 04 2022
(Python)
from itertools import islice
from sympy import factorint
def A356809_gen(): # generator of terms
    a, b = 1, 2
    while True:
        if any(p&3==3 and e&1 for p, e in factorint(a).items()):
            yield a
        a, b = b, a+b
A356809_list = list(islice(A356809_gen(), 30)) # Chai Wah Wu, Jan 10 2023

Crossrefs

Intersection of A000045 and A022544.

Cf. A001481, A022340, A124132, A124134, A236264.

Sequence in context: A039595 A033567 A181156 * A162394 A129212 A354850

Adjacent sequences: A356806 A356807 A356808 * A356810 A356811 A356812

Keyword

nonn

Author

Ctibor O. Zizka, Aug 29 2022

Status

approved