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A174054
Primes of the form x^2+y^2 such that L(x)*L(y) = -1, where L is the Liouville lambda-function A008836.
1
5, 41, 61, 109, 137, 149, 157, 229, 269, 281, 317, 389, 397, 401, 461, 509, 557, 601, 617, 653, 701, 769, 773, 797, 829, 857, 877, 937, 941, 977, 997, 1009, 1013, 1061, 1093, 1097, 1153, 1181, 1213, 1217, 1229, 1249, 1277, 1289, 1321, 1409, 1453, 1489
OFFSET
1,1
EXAMPLE
5 = 1 + 2^2 and L(1)*L(2)= (1) *(-1) = -1.
41 = 4^2 + 5^2 and L(4)*L(5)= (1)*(-1) = -1
MAPLE
isA174054 := proc(n)
local x, y ;
if not isprime(n) then
return false;
end if;
for x from 1 do
if x^2 > n then
return false;
end if;
if issqr(n-x^2) then
y := sqrt(n-x^2) ;
if A008836(x) * A008836(y) = -1 then
return true;
end if;
end if;
end do:
end proc:
for n from 1 to 2000 do
if isA174054(n) then
printf("%d, \n", n) ;
end if;
end do: # R. J. Mathar, Jul 09 2012
MATHEMATICA
lambdaQ[{x_, y_}] := LiouvilleLambda[x]*LiouvilleLambda[y] == -1; Select[ Prime /@ Range[300], Or @@ lambdaQ /@ PowersRepresentations[#, 2, 2] &] (* Jean-François Alcover, Jul 30 2013 *)
CROSSREFS
Sequence in context: A041599 A302692 A232881 * A106963 A276916 A203018
KEYWORD
nonn
AUTHOR
Michel Lagneau, Mar 06 2010
STATUS
approved