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A174053 Prime numbers of the form x^2+y^2 such that Moebius(x)* Moebius(y) = -1 1
5, 61, 109, 149, 157, 229, 269, 317, 389, 397, 461, 509, 557, 653, 701, 773, 797, 877, 941, 997, 1013, 1061, 1093, 1181, 1229, 1277, 1453, 1493, 1613, 1637, 1733, 1877, 1949, 1973, 1997, 2141, 2237, 2309, 2333, 2357, 2477, 2693, 2837, 2909, 2957, 3253 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

All terms == 5 (mod 8). - Robert Israel, May 06 2019

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

5 = 1^2 + 2^2 and Moebius(1)*Moebius(2) = (1) *(-1) = -1.

61 = 5^2 + 6^2 and Moebius(5)*Moebius(6) = (-1)*(1) = -1.

MAPLE

isA174053 := 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 numtheory[mobius](x) * numtheory[mobius](y) = -1 then

                                return true;

                        end if;

                end if;

        end do:

end proc:

for n from 1 to 3000 do

        if isA174053(n) then

                printf("%d, \n", n) ;

        end if;

end do:

# R. J. Mathar, Jul 09 2012

# alternative

N:= 10^5: # to get all terms <= N

SF:= select(numtheory:-issqrfree, [$1..floor(sqrt(N))]):

Mp, Mm:= selectremove(numtheory:-mobius=1, SF):

R:= select(t -> t <= N and isprime(t), {seq(seq(s^2+t^2, s=Mp), t=Mm)}):

sort(convert(R, list)); # Robert Israel, May 06 2019

CROSSREFS

Cf. A008683, A174049, A002313.

Sequence in context: A326726 A141967 A139915 * A107191 A321616 A182352

Adjacent sequences:  A174050 A174051 A174052 * A174054 A174055 A174056

KEYWORD

nonn

AUTHOR

Michel Lagneau, Mar 06 2010

STATUS

approved

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Last modified May 25 11:07 EDT 2020. Contains 334592 sequences. (Running on oeis4.)