A376050 Lexicographically earliest sequence of positive integers a(1), a(2), a(3), ... such that for any n > 0, S(n) = Sum_{k = 1..n} 1/((2*k-1)*a(k)) < 1.

2, 1, 2, 3, 6, 172, 137534, 106557767317, 10018727448950607892211, 218107864753736742334588510315735629277159621, 43040465365773907074907163986022284668974202910116417170603263409796800986397420975160781

Offset: 1

Author

N. J. A. Sloane, Sep 13 2024

Keywords

• nonn
• base

Comments

It appears that S(n) = (e(n)-1)/e(n) for all n != 4, where e(n) = A376051(n). Exceptionally, S(4) = (e(4)-2)/e(4).

a(15) has 1420 decimal digits, too large for a b-file. - Robert Israel, Oct 13 2024

References

• Rémy Sigrist and N. J. A. Sloane, Dampening Down a Divergent Series, Manuscript in preparation, September 2024.

Links

• Robert Israel, Table of n, a(n) for n = 1..14

Crossrefs

Cf. A374663, A375516, A375531, A375532, A375781, A375522, A376048, A376049, A376051.

Programs

Maple

S:= 1:R:= NULL:
for i from 1 to 11 do
  r:= ceil(1/((2*i-1)*S));
  if r *(2*i-1) = 1/S then r:= r+1 fi;
  R:= R,r;
  S:= S - 1/((2*i-1)*r)
od:
R; # Robert Israel, Oct 13 2024