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.

%I A190661 #24 Jul 10 2021 16:24:27
%S A190661 1,7,16,33,52,66,79,72,109,93,121,119,130,153,169,194,180,222,235,275,
%T A190661 294,267,256,296,329,339,333,420,383,373,372,454,396,443,449,504,463,
%U A190661 574,559,512,592,602,596,541,652,585,683,656,687,689,708
%N 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.
%C A190661 All values and even whether the sequence is well defined are conjectural.
%C A190661 a(n) is the conjectured index of the last occurrence of n in A066888.
%C A190661 It is conjectured that for every n >= 0, a(n) > n.
%C A190661 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.
%H A190661 T. D. Noe, <a href="/A190661/b190661.txt">Table of n, a(n) for n = 0..8000</a>
%e A190661 Because it appears that A066888(7) = 1 is the last 1 of that sequence, a(1) = 7.
%Y A190661 Cf. A066888, A000217, A000040, A088634, A104272, A190881.
%K A190661 nonn
%O A190661 0,2
%A A190661 _John W. Nicholson_, May 18 2011
%E A190661 Edited by _T. D. Noe_, May 19 2011