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

0,2

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.

Links

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

Example

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

Crossrefs

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

Sequence in context: A019541 A101426 A296153 * A233058 A301721 A176449

Adjacent sequences: A190658 A190659 A190660 * A190662 A190663 A190664

Keyword

nonn

Author

John W. Nicholson, May 18 2011

Extensions

Edited by T. D. Noe, May 19 2011

Status

approved