A180224 a(n+1) is the least k such that 1/(a(n)+1) + 1/(a(n)+2) + ... + 1/k > 1, with a(1) = 1.

1, 4, 12, 34, 94, 257, 700, 1904, 5177, 14074, 38258, 103997, 282695, 768446, 2088854, 5678095, 15434664, 41955768, 114047603, 310013528, 842704141, 2290707355, 6226788179, 16926165158, 46010087176, 125068383898, 339971115266, 924137304830, 2512065642722, 6828502388509

Offset: 1

Author

Pierre CAMI, Aug 16 2010

Keywords

• nonn

Examples

			1/2 = 0.5, 1/2 + 1/3 = 0.833..., 1/2 + 1/3 + 1/4 = 1.0833... > 1, so a(2) = 4.
		

Crossrefs

Cf. A103762.

Programs

PARI

default(realprecision, 10^5); e=exp(1);
lista(nn) = {my(k=1); print1(k); for(n=2, nn, print1(", ", k=floor(e*k+(e+1)/2+(e-1/e)/(24*(n+1/2))))); } \\ Jinyuan Wang, Mar 05 2020

Formula

a(n) = A103762(a(n-1) + 1) for n > 1. - Jinyuan Wang, Mar 05 2020

Extensions

Name clarified by and more terms from Jinyuan Wang, Mar 05 2020