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

1,1

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.

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. A277719, A164952, A104272, A290394 (first (1 + 1/n)-Ramanujan prime).

Sequence in context: A108294 A046869 A028388 * A067606 A184247 A046135

Adjacent sequences: A277715 A277716 A277717 * A277719 A277720 A277721

Keyword

nonn

Author

John W. Nicholson, Oct 27 2016

Status

approved