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A218217
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a(n) = (x(n+1) - x(n))^2 + (y(n+1) - y(n))^2, where x(n)^2 + y(n)^2 = A055025(n) is norm of Gaussian prime and x(n) >= y(n) >= 0.
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0
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1, 2, 4, 2, 2, 2, 10, 20, 4, 10, 8, 4, 2, 10, 4, 20, 58, 16, 10, 2, 20, 58, 8, 40, 2, 40, 20, 10, 90, 2, 20, 10, 116, 2, 8, 20, 10, 68, 50, 10, 20, 26, 4, 146, 8, 34, 10, 40, 34, 40, 130, 104, 20, 2, 160, 50, 10, 180, 2, 180, 90, 58, 40, 130, 16, 116, 194, 50
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OFFSET
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1,2
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COMMENTS
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We walk through the Gaussian primes in the first octant of the Gaussian plane along increasing norm: 1+i, 2+i, 3, 3+2i, 4+i, 5+2i, 6+i, 5+4i, 7, 7+2i etc. The sequence lists the squared distance between consecutive Gaussian primes along this walk.
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LINKS
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EXAMPLE
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The squared distance between 5+4i and 6+i is (6-5)^2+(4-1)^2 =10 = a(7).
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MATHEMATICA
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nMx = 1000; modLst = {2}; Do[p = Prime[n]; If[Mod[p, 4] == 1, AppendTo[modLst, p], If[p^2 < nMx, AppendTo[modLst, p^2]]], {n, 2, PrimePi[nMx]}]; modLst = Union[modLst]; last = {1, 1}; Table[pr = PowersRepresentations[n, 2, 2][[1]]; dist = SquaredEuclideanDistance[last, pr]; last = pr; dist, {n, Rest[modLst]}] (* T. D. Noe, Oct 29 2012 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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