%I #14 Oct 21 2024 11:47:03
%S 0,1,5,31,247,5891,175669,6639823,290694979,13885515383,746406329689,
%T 44593096214321,3020489689357037,222690147603898211,
%U 17752712881208877899,1486130275559909484787,133315968357656471537153,13025132201814060676912631,2913672358303309675918969343,663425761972477930761347977351,152383524508438692136746106396609
%N a(n) = numerator of Sum_{i=1..n} 1/A038603(i).
%C Numerator of sum of reciprocals of primes with no digit "1".
%C Of interest because it appears that the value of Sum_{i=1..oo} 1/A038603(i) = lim_{i->oo} a(i)/A375534(i) is extremely difficult to compute - so difficult that its decimal expansion does not have an OEIS entry. (Compare A082830.)
%H Alois P. Heinz, <a href="/A375533/b375533.txt">Table of n, a(n) for n = 0..313</a>
%H N. J. A. Sloane, <a href="https://www.youtube.com/watch?v=3RAYoaKMckM">A Nasty Surprise in a Sequence and Other OEIS Stories</a>, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; <a href="https://sites.math.rutgers.edu/~zeilberg/expmath/sloane85BD.pdf">Slides</a> [Mentions this sequence]
%e The first few sums are 0/1, 1/2, 5/6, 31/30, 247/210, 5891/4830, 175669/140070, 6639823/5182590, ...
%t a[n_]:=Numerator[Sum[ 1/Part[ResourceFunction["OEISSequence"]["A038603"],i],{i,n}]]; Array[a,20] (* _Stefano Spezia_, Sep 06 2024 *)
%Y Cf. A024451, A038603, A375534, A082830.
%K nonn,base,frac
%O 0,3
%A _N. J. A. Sloane_, Sep 06 2024
%E a(0) prepended by _Alois P. Heinz_, Oct 21 2024