A080148 Positions of primes of the form 4*k+3 (A002145) among all primes (A000040).

2, 4, 5, 8, 9, 11, 14, 15, 17, 19, 20, 22, 23, 27, 28, 31, 32, 34, 36, 38, 39, 41, 43, 46, 47, 48, 49, 52, 54, 56, 58, 61, 63, 64, 67, 69, 72, 73, 75, 76, 81, 83, 85, 86, 90, 91, 92, 93, 94, 95, 96, 99, 101, 103, 105, 107, 109, 111, 114, 115, 117, 118, 120, 124, 125, 128

Offset: 1

Author

Antti Karttunen, Feb 11 2003

Keywords

• nonn

Comments

It appears that a(n) = k such that binomial(prime(k),3) mod 2 = 1. See Maple code. - Gary Detlefs, Dec 06 2011

The above is correct (work mod 4). - Charles R Greathouse IV, Dec 06 2011

The asymptotic density of this sequence is 1/2 (by Dirichlet's theorem). - Amiram Eldar, Mar 01 2021

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000

Crossrefs

Almost complement of A080147 (1 is excluded from both).

Cf. A000040, A002145, A049084.

Programs

Maple

pos_of_primes_k_mod_n(300,3,4); # Given in A080147.
A080148 := proc(n)
        numtheory[pi](A002145(n)) ;
end proc:
seq(A080148(n),n=1..40) ; # R. J. Mathar, Dec 08 2011

Mathematica

Flatten[Position[Prime[Range[200]],?(IntegerQ[(#-3)/4]&)]] (* _Harvey P. Dale, Jun 06 2011 *)
Select[Range[135], Mod[Prime[#], 4] == 3 &] (* Amiram Eldar, Mar 01 2021 *)

PARI

i=0;forprime(p=2,1e3,i++;if(p%4==3,print1(i", "))) \\ Charles R Greathouse IV, Dec 06 2011

Formula

a(n) = A049084(A002145(n)). - R. J. Mathar, Oct 06 2008