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Number of primes of the form 4m+3 that are <= n.
9

%I #16 Oct 22 2021 12:40:04

%S 0,0,1,1,1,1,2,2,2,2,3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,

%T 6,6,6,6,6,6,6,6,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,9,9,9,9,9,9,9,9,10,

%U 10,10,10,11,11,11,11,11,11,11,11,12,12,12,12,13,13,13,13,13,13,13,13,13

%N Number of primes of the form 4m+3 that are <= n.

%C Partial sums of A079261. - _Reinhard Zumkeller_, Feb 06 2014

%H T. D. Noe, <a href="/A066490/b066490.txt">Table of n, a(n) for n=1..10000</a>

%F A066339(n) + a(n) = A000720(n) - 1 for n >= 2. - _Jianing Song_, Apr 28 2021

%t Table[ Length[ Select[ Union[ Table[ Prime[ PrimePi[i]], {i, 2, n}]], Mod[ #, 4] == 3 & ]], {n, 2, 100} ]

%t Accumulate[Table[If[PrimeQ[n]&&Mod[n,4]==3,1,0],{n,100}]] (* _Harvey P. Dale_, Mar 17 2021 *)

%o (PARI) for(n=1,100,print1(sum(i=1,n,if((i*isprime(i)-3)%4,0,1)),","))

%o (Haskell)

%o a066490 n = a066490_list !! (n-1)

%o a066490_list = scanl1 (+) $ map a079261 [1..]

%o -- _Reinhard Zumkeller_, Feb 06 2014

%Y Cf. A000720, A066339, A296020.

%K easy,nonn

%O 1,7

%A _Robert G. Wilson v_, Jan 03 2002