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A277718 Bounding prime for the first k-Ramanujan prime. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 10 23:33 EST 2018. Contains 318049 sequences. (Running on oeis4.)