A277718 Bounding prime for the first k-Ramanujan prime.

5, 11, 17, 29, 37, 53, 127, 149, 211, 223, 307, 331, 541, 1361, 1693, 1973, 2203, 2503, 2999, 3299, 4327, 4861, 5623, 5779, 5981, 6521, 6947, 7283, 8501, 9587, 10007, 10831, 11777, 15727, 19661, 31469, 34123, 35671, 35729, 43391, 44351, 45943, 48731, 58889

Offset: 1

Author

John W. Nicholson, Oct 27 2016

Keywords

• nonn

Comments

The index A277719(n) is h(n), the prime a(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. A277719, A164952, A104272, A290394 (first (1 + 1/n)-Ramanujan prime).