cp's OEIS Frontend

A269364 Difference between the number of occurrences of prime gaps not divisible by 3, versus number of prime gaps that are multiples of 3, up to n-th prime gap: a(n) = A269849(n) - A269850(n).

%I A269364 #23 Feb 10 2018 19:41:51
%S A269364 1,2,3,4,5,6,7,8,7,8,7,8,9,10,9,8,9,8,9,10,9,10,9,10,11,12,13,14,15,
%T A269364 16,17,16,17,18,19,18,17,18,17,16,17,18,19,20,21,20,19,20,21,22,21,22,
%U A269364 23,22,21,20,21,20,21,22,23,24,25,26,27,28,27,28,29,30,29,30,29,28,29,28,29,30,31,32,33,34,35,34
%N A269364 Difference between the number of occurrences of prime gaps not divisible by 3, versus number of prime gaps that are multiples of 3, up to n-th prime gap: a(n) = A269849(n) - A269850(n).
%C A269364 This is related to "Lemke Oliver-Soundararajan bias", term first used by Terence Tao March 14, 2016 in his blog.
%H A269364 Antti Karttunen, <a href="/A269364/b269364.txt">Table of n, a(n) for n = 1..50000</a>
%H A269364 Robert J. Lemke Oliver and Kannan Soundararajan, <a href="http://arxiv.org/abs/1603.03720">Unexpected biases in the distribution of consecutive primes</a>, arXiv:1603.03720 [math.NT], 2016.
%H A269364 Terence Tao, <a href="https://terrytao.wordpress.com/2016/03/14/biases-between-consecutive-primes/">Biases between consecutive primes</a>, blog entry March 14, 2016
%F A269364 a(n) = A269849(n) - A269850(n).
%o A269364 (Scheme) (define (A269364 n) (- (A269849 n) (A269850 n)))
%o A269364 (PARI) a(n) = sum(k=1, n, ((prime(k+1) - prime(k)) % 3) != 0) - sum(k=1, n, ((prime(k+1) - prime(k)) % 3) == 0); \\ _Michel Marcus_, Mar 18 2016
%Y A269364 Cf. A001223, A137264, A269849, A269850, A270189, A270190.
%Y A269364 Cf. also A270310, A038698.
%K A269364 nonn
%O A269364 1,2
%A A269364 _Antti Karttunen_, Mar 17 2016