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

Author

John W. Nicholson, Oct 27 2016

Keywords

• nonn

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.

Examples

			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).
		

Links

• 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.

Crossrefs

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