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

%I A358311 #24 Jan 26 2024 13:53:36
%S A358311 3,7,11,47,76,123,199,322,843,1364,2207,3571,5778,15127,24476,39603,
%T A358311 64079,103682,167761,271443,439204,710647,1149851,4870847,7881196,
%U A358311 12752043,20633239,33385282,87403803,141422324,228826127,370248451,599074578,1568397607,2537720636
%N A358311 Lucas numbers that are not the sum of two squares.
%C A358311 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 A358311 Chai Wah Wu, <a href="/A358311/b358311.txt">Table of n, a(n) for n = 1..958</a>
%F A358311 phi^n < a(n) < phi^(2n) for n > 4. - _Charles R Greathouse IV_, Jan 11 2023
%p A358311 R:= NULL: count:= 0:
%p A358311 a:= 2: b:= 1:
%p A358311 for i from 1 while count < 100 do
%p A358311   a, b:= b,a+b;
%p A358311     if ormap(t -> t[2]::odd and t[1] mod 4 = 3, ifactors(b)[2]) then
%p A358311      R:= R, b; count:= count+1
%p A358311   fi
%p A358311 od:
%p A358311 R; # _Robert Israel_, Jan 10 2023
%o A358311 (Python)
%o A358311 from sympy import factorint
%o A358311 from itertools import islice
%o A358311 def A358311_gen(): # generator of terms
%o A358311     a, b = 2,1
%o A358311     while True:
%o A358311         if any(e&1 and p&3==3 for p, e in factorint(a).items()):
%o A358311             yield a
%o A358311         a, b = b, a+b
%o A358311 A358311_list = list(islice(A358311_gen(),40))
%Y A358311 Intersection of A000032 and A022544.
%Y A358311 Cf. A356809.
%K A358311 nonn
%O A358311 1,1
%A A358311 _Chai Wah Wu_, Jan 10 2023