

A190661


Least number a(n) such that there are at least n primes in the range (T(k1), T(k)] for all k >= a(n), where T(k) is the kth triangular number.


8



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
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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 nth 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



