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A080148
Positions of primes of the form 4*k+3 (A002145) among all primes (A000040).
17
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
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).
Sequence in context: A096603 A084464 A289008 * A241572 A032787 A067366
KEYWORD
nonn
AUTHOR
Antti Karttunen, Feb 11 2003
STATUS
approved