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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).
9
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, 16, 17, 16, 17, 18, 19, 18, 17, 18, 17, 16, 17, 18, 19, 20, 21, 20, 19, 20, 21, 22, 21, 22, 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
OFFSET
1,2
COMMENTS
This is related to "Lemke Oliver-Soundararajan bias", term first used by Terence Tao March 14, 2016 in his blog.
LINKS
Robert J. Lemke Oliver and Kannan Soundararajan, Unexpected biases in the distribution of consecutive primes, arXiv:1603.03720 [math.NT], 2016.
Terence Tao, Biases between consecutive primes, blog entry March 14, 2016
FORMULA
a(n) = A269849(n) - A269850(n).
PROG
(Scheme) (define (A269364 n) (- (A269849 n) (A269850 n)))
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Mar 17 2016
STATUS
approved