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

Author

John W. Nicholson, May 18 2011

Keywords

• nonn

Comments

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.

Examples

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

Links

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

Crossrefs

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

Extensions

Edited by T. D. Noe, May 19 2011