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

1,1

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

Formula

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

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 *)

Prog

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

Crossrefs

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

Cf. A000040, A002145, A049084.

Sequence in context: A096603 A084464 A289008 * A241572 A032787 A067366

Adjacent sequences: A080145 A080146 A080147 * A080149 A080150 A080151

Keyword

nonn

Author

Antti Karttunen, Feb 11 2003

Status

approved