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A077767
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Number of primes of form 4k+3 between n^2 and (n+1)^2.
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6
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1, 1, 1, 2, 1, 2, 1, 3, 1, 2, 3, 3, 2, 3, 3, 3, 2, 3, 3, 3, 4, 5, 3, 4, 4, 4, 3, 5, 4, 4, 5, 5, 4, 4, 5, 5, 4, 8, 8, 5, 4, 6, 5, 6, 7, 5, 5, 7, 5, 7, 7, 7, 6, 8, 4, 5, 11, 5, 9, 8, 6, 11, 7, 7, 7, 7, 8, 10, 5, 12, 10, 5, 9, 10, 7, 13, 8, 8, 11, 5, 10, 9, 13, 9, 6, 9, 12, 7, 7, 11, 10, 9, 12, 11, 10, 10
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OFFSET
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1,4
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COMMENTS
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Related to Legendre's conjecture that there is always a prime between two consecutive squares.
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LINKS
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EXAMPLE
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a(8)=3 because primes 67, 71 and 79 are between squares 64 and 81
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MATHEMATICA
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maxN=100; a=Table[0, {maxN}]; maxP=PrimePi[(maxN+1)^2]; For[i=1, i<=maxP, i++, p=Prime[i]; If[Mod[p, 4]==3, j=Floor[Sqrt[p]]; a[[j]]++ ]]; a
p3[{a_, b_}]:=Module[{p=Prime[Range[PrimePi[a]+1, PrimePi[b]]]}, Count[p, _?(Mod[#, 4]==3&)]]; p3/@Partition[Range[100]^2, 2, 1] (* Harvey P. Dale, Feb 20 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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STATUS
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approved
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