A241189 Numerator of Sum_{i=1..n} 1/(prime(i)*prime(i+1)).

1, 7, 11, 127, 1693, 29243, 561623, 13019431, 379503437, 11809225121, 438235268123, 18007758091069, 775817745542929, 36524284093223105, 1938403609207158571, 2160165866032831207, 131893095784520401909, 8844093116997411126541, 628373208972323386101329, 45900898298568589325230523

Offset: 1

Author

N. J. A. Sloane, Apr 25 2014, based on a suggestion from Timothy Varghese

Keywords

• nonn
• frac

Comments

a(371) has 1002 decimal digits. - Michael De Vlieger, Jan 27 2016

Examples

			1/6, 7/30, 11/42, 127/462, 1693/6006, 29243/102102, 561623/1939938, 13019431/44618574, 379503437/1293938646, 11809225121/40112098026, 438235268123/1484147626962, ...
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..370

Crossrefs

Cf. A024451/A002110, A241189/A241190, A241191/A241192.

See also A061015/A061742, A115963/A115964.

Programs

Maple

g:= n-> add(1/(ithprime(i)*ithprime(i+1)),i=1..n);
t1:=[seq(g(n),n=1..20)];
t1a:=map(numer,t1); # A241189
t1b:=map(denom,t1); # A241190

Mathematica

Table[Numerator@ Sum[1/(Prime[i + 1] Prime@ i), {i, n}], {n, 20}] (* Michael De Vlieger, Jan 27 2016 *)
Accumulate[1/#&/@(Times@@@Partition[Prime[Range[25]],2,1])]//Numerator (* Harvey P. Dale, Mar 14 2023 *)