A331930 a(n) is the smallest composite k such that Sum_{composites j = 4, ..., k} 1/j exceeds n/2.

8, 16, 33, 63, 118, 216, 395, 715, 1281, 2279, 4036, 7102, 12441, 21722, 37797, 65558, 113422, 195759, 337148, 579465, 994194, 1703072, 2912869, 4975222, 8486672, 14459492, 24608418, 41837580, 71060409, 120585504, 204452804, 346372172, 586359050, 991915208

Offset: 1

Author

Jon E. Schoenfield, Feb 01 2020

Keywords

• nonn

Comments

Lim_{n->infinity} a(n+1)/a(n) = sqrt(e).

Examples

			a(1) = 1 because 1/4 + 1/6 = 0.41666... < 1/2 but 1/4 + 1/6 + 1/8 = 0.54166... > 1/2.
		

Crossrefs

Cf. A016088 (sum of reciprocals of primes exceeds n), A076751 (sum of reciprocals of composites exceeds n), A103592 (sum of reciprocals of primes exceeds n/2).

Cf. A019774 (sqrt(e)).

Formula

a(2n) = A076751(n).