

A190661


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



EXAMPLE

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


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



