A358311 - OEIS

%I #24 Jan 26 2024 13:53:36

%S 3,7,11,47,76,123,199,322,843,1364,2207,3571,5778,15127,24476,39603,

%T 64079,103682,167761,271443,439204,710647,1149851,4870847,7881196,

%U 12752043,20633239,33385282,87403803,141422324,228826127,370248451,599074578,1568397607,2537720636

%N Lucas numbers that are not the sum of two squares.

%C 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

%H Chai Wah Wu, <a href="/A358311/b358311.txt">Table of n, a(n) for n = 1..958</a>

%F phi^n < a(n) < phi^(2n) for n > 4. - _Charles R Greathouse IV_, Jan 11 2023

%p R:= NULL: count:= 0:

%p a:= 2: b:= 1:

%p for i from 1 while count < 100 do

%p   a, b:= b,a+b;

%p     if ormap(t -> t[2]::odd and t[1] mod 4 = 3, ifactors(b)[2]) then

%p      R:= R, b; count:= count+1

%p   fi

%p od:

%p R; # _Robert Israel_, Jan 10 2023

%o (Python)

%o from sympy import factorint

%o from itertools import islice

%o def A358311_gen(): # generator of terms

%o     a, b = 2,1

%o     while True:

%o         if any(e&1 and p&3==3 for p, e in factorint(a).items()):

%o             yield a

%o         a, b = b, a+b

%o A358311_list = list(islice(A358311_gen(),40))

%Y Intersection of A000032 and A022544.

%Y Cf. A356809.

%K nonn

%O 1,1

%A _Chai Wah Wu_, Jan 10 2023