A174054 Primes of the form x^2+y^2 such that L(x)*L(y) = -1, where L is the Liouville lambda-function A008836.

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

Links

Table of n, a(n) for n=1..48.

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

Cf. A174050, A002313.

Sequence in context: A041599 A302692 A232881 * A106963 A276916 A203018

Adjacent sequences: A174051 A174052 A174053 * A174055 A174056 A174057

Keyword

nonn

Author

Michel Lagneau, Mar 06 2010

Status

approved