A066490 Number of primes of the form 4m+3 that are <= n.

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, 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, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13

Offset: 1

Author

Robert G. Wilson v, Jan 03 2002

Keywords

• easy
• nonn

Comments

Partial sums of A079261. - Reinhard Zumkeller, Feb 06 2014

Links

• T. D. Noe, Table of n, a(n) for n=1..10000

Crossrefs

Cf. A000720, A066339, A296020.

Programs

Haskell

a066490 n = a066490_list !! (n-1)
a066490_list = scanl1 (+) $ map a079261 [1..]
-- Reinhard Zumkeller, Feb 06 2014

Mathematica

Table[ Length[ Select[ Union[ Table[ Prime[ PrimePi[i]], {i, 2, n}]], Mod[ #, 4] == 3 & ]], {n, 2, 100} ]
Accumulate[Table[If[PrimeQ[n]&&Mod[n,4]==3,1,0],{n,100}]] (* Harvey P. Dale, Mar 17 2021 *)

PARI

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

Formula

A066339(n) + a(n) = A000720(n) - 1 for n >= 2. - Jianing Song, Apr 28 2021