A358311 Lucas numbers that are not the sum of two squares.

3, 7, 11, 47, 76, 123, 199, 322, 843, 1364, 2207, 3571, 5778, 15127, 24476, 39603, 64079, 103682, 167761, 271443, 439204, 710647, 1149851, 4870847, 7881196, 12752043, 20633239, 33385282, 87403803, 141422324, 228826127, 370248451, 599074578, 1568397607, 2537720636

Offset

1,1

Comments

Lucas numbers with indices 2, 4, 5 mod 6 are 3 mod 4, so these are all terms. - Charles R Greathouse IV, Jan 11 2023

Links

Chai Wah Wu, Table of n, a(n) for n = 1..958

Formula

phi^n < a(n) < phi^(2n) for n > 4. - Charles R Greathouse IV, Jan 11 2023

Maple

R:= NULL: count:= 0:
a:= 2: b:= 1:
for i from 1 while count < 100 do
  a, b:= b, a+b;
    if ormap(t -> t[2]::odd and t[1] mod 4 = 3, ifactors(b)[2]) then
     R:= R, b; count:= count+1
  fi
od:
R; # Robert Israel, Jan 10 2023

Prog

(Python)
from sympy import factorint
from itertools import islice
def A358311_gen(): # generator of terms
    a, b = 2, 1
    while True:
        if any(e&1 and p&3==3 for p, e in factorint(a).items()):
            yield a
        a, b = b, a+b
A358311_list = list(islice(A358311_gen(), 40))

Crossrefs

Intersection of A000032 and A022544.

Cf. A356809.

Sequence in context: A139599 A141161 A333421 * A217383 A005372 A125220

Adjacent sequences: A358308 A358309 A358310 * A358312 A358313 A358314

Keyword

nonn

Author

Chai Wah Wu, Jan 10 2023

Status

approved