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A211280
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Numerator of prime(n+1) - prime(n)/2.
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2
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2, 7, 9, 15, 15, 21, 21, 27, 35, 33, 43, 45, 45, 51, 59, 65, 63, 73, 75, 75, 85, 87, 95, 105, 105, 105, 111, 111, 117, 141, 135, 143, 141, 159, 153, 163, 169, 171, 179, 185, 183, 201, 195, 201, 201, 223, 235, 231, 231, 237, 245, 243, 261, 263, 269, 275, 273, 283, 285, 285, 303, 321, 315, 315, 321, 345, 343, 357, 351, 357, 365, 375, 379
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OFFSET
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1,1
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COMMENTS
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Second row of the inverse semi-binomial transform of A000040(n+1) as introduced in A213268.
The list of denominators is 1, 2, 2, ... (2 repeated), so a(n) = A210497(n) for n>1.
a(n) - prime(n) = 2*prime(n+1)-prime(n)-prime(n) are prime differences (A001223) multiplied by 2, and therefore multiples of 4.
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LINKS
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FORMULA
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MAPLE
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ithprime(n+1)-ithprime(n)/2 ;
numer(%) ;
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MATHEMATICA
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Numerator[#[[2]]-#[[1]]/2]&/@Partition[Prime[Range[80]], 2, 1] (* Harvey P. Dale, Mar 05 2023 *)
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CROSSREFS
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KEYWORD
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nonn,easy,frac
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AUTHOR
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STATUS
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approved
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