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A079952 Number of primes less than prime(n)/2. 5

%I

%S 0,0,1,2,3,3,4,4,5,6,6,7,8,8,9,9,10,10,11,11,11,12,13,14,15,15,15,16,

%T 16,16,18,18,19,19,21,21,21,22,23,23,24,24,24,24,25,25,27,29,30,30,30,

%U 30,30,30,31,32,32,32,33,34,34,34,36,36,36,37,38,39,40

%N Number of primes less than prime(n)/2.

%C Previous name: Number of primes p such that prime(n) mod 2*p < prime(n).

%C Same as A055930, except for a(2). [Noticed by _R. J. Mathar_, Dec 15 2008, proved by _Andrey Zabolotskiy_, Oct 26 2017]

%F A079950(n, a(n) + 1) = prime(n).

%F Where defined, that is for n > 2, prime(a(n)) = A055377(prime(n)). - _Peter Munn_, Sep 18 2017

%F 0 with partial sums of A217564. - _David A. Corneth_, Oct 26 2017 (found earlier by _Peter Munn_).

%e n = 6: prime(6) = 13 and 2, 3, 5 are less than 13/2, therefore a(6) = 3.

%t Table[PrimePi[Prime[n]/2], {n, 75}] (* _Michael De Vlieger_, Sep 20 2017 *)

%o (PARI) a(n) = primepi(prime(n)/2); \\ _Michel Marcus_, Sep 20 2017

%Y Cf. A000040, A000720, A055377, A055930, A079951, A079953, A217564.

%K nonn

%O 1,4

%A _Reinhard Zumkeller_, Jan 19 2003

%E New name from _Peter Munn_, Sep 18 2017

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Last modified January 19 20:41 EST 2020. Contains 331066 sequences. (Running on oeis4.)