A139338 Least k > 0 such that Sum_{i=0..2*n-1} (-k)^i/i! < 0.

1, 2, 3, 3, 4, 4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 11, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 20, 20, 21, 21, 22, 22, 23, 24, 24, 25, 25, 26, 26, 27, 27, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38, 39, 39, 40, 40, 41, 41, 42, 43

Offset: 1

Author

Benoit Cloitre, Jun 08 2008

Keywords

• nonn

References

• Serge Francinou, Herve Gianella and Serge Nicolas, Exercices de mathématiques : oraux X-ENS, Analyse 1, Cassini Editeur, 2003, pp. 119-121.

Crossrefs

Cf. A030178.

Programs

PARI

a(n)=if(n<0,0,k=1;while(sum(i=0,2*n-1,(-k)^i*1./i!)>0,k++);k)

Formula

a(n) = r*n + o(n) where r is the solution to x + log(x) = 0 and 0 < x < 1: r = 0.56714329040978387299996... (see A030178).