

A277718


Bounding prime for the first kRamanujan 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
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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 kRamanujan 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 kRamanujan prime, arXiv:1504.05485 [math.NT], 2015.
Christian Axler and Thomas Leßmann, On the first kRamanujan prime, Amer. Math. Monthly, 124 (2017), 642646.


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



