A375533 a(n) = numerator of Sum_{i=1..n} 1/A038603(i).

0, 1, 5, 31, 247, 5891, 175669, 6639823, 290694979, 13885515383, 746406329689, 44593096214321, 3020489689357037, 222690147603898211, 17752712881208877899, 1486130275559909484787, 133315968357656471537153, 13025132201814060676912631, 2913672358303309675918969343, 663425761972477930761347977351, 152383524508438692136746106396609

Offset: 0

Author

N. J. A. Sloane, Sep 06 2024

Keywords

• nonn
• base
• frac

Comments

Numerator of sum of reciprocals of primes with no digit "1".

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.)

Examples

			The first few sums are 0/1, 1/2, 5/6, 31/30, 247/210, 5891/4830, 175669/140070, 6639823/5182590,  ...
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..313
• N. J. A. Sloane, A Nasty Surprise in a Sequence and Other OEIS Stories, Experimental Mathematics Seminar, Rutgers University, Oct 10 2024, Youtube video; Slides [Mentions this sequence]

Crossrefs

Cf. A024451, A038603, A375534, A082830.

Programs

Mathematica

a[n_]:=Numerator[Sum[ 1/Part[ResourceFunction["OEISSequence"]["A038603"],i],{i,n}]]; Array[a,20] (* Stefano Spezia, Sep 06 2024 *)

Extensions

a(0) prepended by Alois P. Heinz, Oct 21 2024