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A277719 Index for the bound for the first k-Ramanujan prime. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 16 19:48 EST 2022. Contains 350376 sequences. (Running on oeis4.)