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Accumulate[1/#&/@(Times@@@Partition[Prime[Range[25]], 2, 1])]//Numerator (* Harvey P. Dale, Mar 14 2023 *)
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Numerator of Sum_{i=1..n} 1/((prime(i)*prime(i+1)).
a(371) has 1002 decimal digits. - Michael De Vlieger, Jan 27 2016
Michael De Vlieger, <a href="/A241189/b241189.txt">Table of n, a(n) for n = 1..370</a>
Table[Numerator@ Sum[1/(Prime[i + 1] Prime@ i), {i, n}], {n, 20}] (* Michael De Vlieger, Jan 27 2016 *)
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N. J. A. Sloane, Apr 25 2014, based on a suggestion from _Tim Timothy Varghese_.
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