A088634 -id:A088634 - cp's OEIS frontend

A190661 a(n) is the least number m such that there are at least n primes in the range (T(k-1), T(k)] for all k >= m, where T(k) is the k-th triangular number.

1, 7, 16, 33, 52, 66, 79, 72, 109, 93, 121, 119, 130, 153, 169, 194, 180, 222, 235, 275, 294, 267, 256, 296, 329, 339, 333, 420, 383, 373, 372, 454, 396, 443, 449, 504, 463, 574, 559, 512, 592, 602, 596, 541, 652, 585, 683, 656, 687, 689, 708

Offset: 0

John W. Nicholson, May 18 2011

nonn

All values and even whether the sequence is well defined are conjectural.
a(n) is the conjectured index of the last occurrence of n in A066888.
It is conjectured that for every n >= 0, a(n) > n.
With R_n the n-th Ramanujan prime (A104272), it is conjectured that for every n >= 0, (1/2) R_n <= a(n) < (20/13) R_n. These bounds have been verified for all n up to 8000. For most n <= 8000, we have a(n) > R_n, with exceptions listed in A190881.

			Because it appears that A066888(7) = 1 is the last 1 of that sequence, a(1) = 7.

T. D. Noe, Table of n, a(n) for n = 0..8000

Cf. A066888, A000217, A000040, A088634, A104272, A190881.

Edited by T. D. Noe, May 19 2011

A190881 Exception list of where A190661(n) < A104272(n) for n > 0.

Original entry on oeis.org

43, 45, 68, 93, 145, 341, 655, 3177, 3383, 3424, 4696, 5109, 5116, 5183, 5201, 5225, 7195, 7574

Offset: 1

John W. Nicholson, May 23 2011

nonn

a(n) is the value of n of A190661 and A104272 at the exception.

Cf. A066888, A000217, A000040, A088634, A190661, A104272.

Corrected data for the changed offset and data of A190661 - John W. Nicholson, Nov 20 2013

cp's OEIS Frontend

A190661 a(n) is the least number m such that there are at least n primes in the range (T(k-1), T(k)] for all k >= m, where T(k) is the k-th triangular number.

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