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a(n) is the difference between the number of primes smaller than prime(n) (i.e., n-1) and greater than prime(n) but less than 2*prime(n).
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%I #18 Oct 09 2020 09:03:32

%S -1,0,1,1,1,2,2,3,3,3,3,2,3,4,5,4,3,5,5,5,7,6,7,7,5,5,7,8,10,11,7,8,7,

%T 8,7,9,8,9,10,11,10,11,10,11,12,13,11,9,10,11,11,12,13,12,12,12,14,15,

%U 16,17,18,17,13,13,15,16,12,13,12,14,15,16,15,15

%N a(n) is the difference between the number of primes smaller than prime(n) (i.e., n-1) and greater than prime(n) but less than 2*prime(n).

%F a(n) = (2*n-1) - A020900(n). - _Michel Marcus_, Feb 02 2020

%F a(n) = n - 1 - A070046(n). - _M. F. Hasler_, Feb 29 2020

%F a(n) = A334051(n) - 1. - _Alois P. Heinz_, Oct 09 2020

%o (PARI) a(n) = 2*n - 1 - primepi(2*prime(n)); \\ _Michel Marcus_, Feb 02 2020

%Y Cf. A000040, A000720, A020900, A070046, A334051.

%K sign

%O 1,6

%A _Todor Szimeonov_, Jan 24 2020