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A174049
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Prime numbers of the form x^2+y^2 such that Mobius(x) * Mobius(y) = 1.
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2
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2, 13, 29, 37, 53, 101, 173, 197, 293, 421, 541, 677, 709, 1021, 1069, 1117, 1373, 1381, 1429, 1597, 1621, 1669, 1709, 1741, 1789, 1861, 1901, 1933, 2053, 2213, 2269, 2293, 2341, 2381, 2557, 2677, 2749, 2797, 3061, 3109, 3221, 3613, 3637, 3701
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OFFSET
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1,1
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 844.
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LINKS
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
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EXAMPLE
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2 is in the sequence because 2 = 1^2 + 1^2 and mobius(1)*mobius(1) = 1*1 = 1;
13 is a term because 13 = 2^2 + 3^2 and mobius(2)*mobius(3) = (-1)*(-1) = 1.
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MAPLE
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with(numtheory): T:=array(0..50000000): k:=1:for x from 1 to 1000 do: for y from x to 1000 do if mobius(x)* mobius(y)= 1 and isprime(x^2+y^2) then T[k]:=x^2+y^2:k:=k+1 fi od od: mini:=T[1]:ii:=1: for p from 1 to k-1 do for n from 1 to k-1 do if T[n] < mini then mini:= T[n]:ii:=n fi od: print(mini): T[ii]:= 99999999: ii:=1:mini:=T[1] :od:
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MATHEMATICA
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terms = 1000;
Reap[Do[p = x^2 + y^2; If[PrimeQ[p] && MoebiusMu[x] MoebiusMu[y] == 1, Sow[p]], {x, terms}, {y, x}]][[2, 1]] // Sort // Take[#, terms]& (* Jean-François Alcover, Aug 31 2020 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Typo in name and missing value inserted by D. S. McNeil, Nov 20 2010
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STATUS
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approved
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