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A161846
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Numerator of the ratio (prime((n+1)^2) - prime(n^2))/prime(n).
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2
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5, 16, 6, 44, 54, 76, 84, 108, 122, 120, 166, 182, 184, 234, 192, 260, 264, 294, 304, 342, 378, 342, 408, 426, 414, 468, 488, 474, 516, 576, 588, 576, 604, 590, 696, 694, 728, 694, 756, 828, 774, 776, 870, 862, 852, 1010, 922, 998, 916, 1020, 1032, 1110, 1104
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OFFSET
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1,1
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COMMENTS
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Conjecture: the sequence of fractions (prime((n+1)^2) - prime(n^2)) / prime(n) converges to 4. There are several "heuristic demonstrations" but no proofs.
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LINKS
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FORMULA
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EXAMPLE
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The first few fractions are 5/2, 16/3, 6/1, 44/7, 54/11, ...= A161846/A161847.
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MAPLE
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A161846 := proc(n) ( ithprime((n+1)^2)-ithprime(n^2))/ithprime(n) ; numer(%) ; end: seq(A161846(n), n=1..25) ; # R. J. Mathar, Jun 22 2009
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MATHEMATICA
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Table[(Prime[(n+1)^2]-Prime[n^2])/Prime[n], {n, 60}]//Numerator (* Harvey P. Dale, Oct 24 2017 *)
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PROG
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(PARI) a(n) = numerator((prime((n+1)^2) - prime(n^2))/prime(n)); \\ Michel Marcus, May 14 2020
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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