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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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Jul 30 2013 *)

CROSSREFS

Cf. A174050, A002313.

Sequence in context: A043083 A041599 A232881 * A106963 A276916 A203018

Adjacent sequences:  A174051 A174052 A174053 * A174055 A174056 A174057

KEYWORD

nonn

AUTHOR

Michel Lagneau, Mar 06 2010

STATUS

approved

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Last modified August 18 18:12 EDT 2017. Contains 290732 sequences.