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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
2, 1, 2, 3, 6, 172, 137534, 106557767317, 10018727448950607892211, 218107864753736742334588510315735629277159621, 43040465365773907074907163986022284668974202910116417170603263409796800986397420975160781
OFFSET
1,1
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
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
KEYWORD
nonn,base
AUTHOR
N. J. A. Sloane, Sep 13 2024
STATUS
approved