A103592 -id:A103592 - cp's OEIS frontend

A103591 Smallest number m such that Sum_{k=1..m} 1/prime(k) >= n/2.

1, 3, 10, 59, 1413, 361139, 4833601540, 43922730588128390

Offset: 1

James R. Buddenhagen, Mar 28 2005

Table[m = 1; s = 0; While[(s = s + 1/Prime[m]) < n/2, m++];
m, {n, 1, 5}] (* Robert Price, Mar 27 2019 *)

a(n) = my(s = 0, k = 1); while ((s += 1/prime(k)) < n/2, k++); k \\ Michel Marcus, Aug 22 2013

a(2n) = A046024(n). - Michel Marcus, Aug 22 2013

a(7) from Robert Price, Dec 10 2013

a(8) derived from A046024 by Robert Price, Dec 10 2013

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

Original entry on oeis.org

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

Jon E. Schoenfield, Feb 01 2020

nonn

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

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

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)).

a(2n) = A076751(n).

cp's OEIS Frontend

A103591 Smallest number m such that Sum_{k=1..m} 1/prime(k) >= n/2.

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