A277719 Index for the bound for the first k-Ramanujan prime.

3, 5, 7, 10, 12, 16, 31, 35, 47, 48, 63, 67, 100, 218, 264, 298, 328, 368, 430, 463, 591, 651, 739, 758, 782, 843, 891, 929, 1060, 1184, 1230, 1316, 1410, 1832, 2226, 3386, 3645, 3794, 3796, 4523, 4613, 4755, 5009, 5950

Offset

1,1

Comments

The index a(n) is h(n), the prime A277718(n) is p_h(n). If 1 <= n <= 43 and k in [p_{h(n+1)}/p_{h(n+1)-1}, p_{h(n)}/p_{h(n)-1}), then the first k-Ramanujan prime R^{(k)}_1 = p_{h(n)}. Extra terms require improvements of prime numbers in short intervals.

Links

Table of n, a(n) for n=1..44.

Christian Axler and Thomas Leßmann, An explicit upper bound for the first k-Ramanujan prime, arXiv:1504.05485 [math.NT], 2015.

Christian Axler and Thomas Leßmann, On the first k-Ramanujan prime, Amer. Math. Monthly, 124 (2017), 642-646.

Example

With n = 3, we see p_h(3) = 17, p_h(4) = 29, so that 29/23 <= k < 17/13. If k = 1.3 then R^(1.3)_1 = 17 = p_h(3).

Crossrefs

Cf. A277718, A164952, A104272, A290394 (first (1 + 1/n)-Ramanujan prime).

Sequence in context: A335408 A211266 A037030 * A251553 A075782 A050090

Adjacent sequences: A277716 A277717 A277718 * A277720 A277721 A277722

Keyword

nonn

Author

John W. Nicholson, Oct 27 2016

Status

approved