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A358311
Lucas numbers that are not the sum of two squares.
1
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
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
KEYWORD
nonn
AUTHOR
Chai Wah Wu, Jan 10 2023
STATUS
approved