A163595 Numbers k such that prime(k) == 5 (mod 9).

3, 9, 13, 17, 30, 32, 35, 39, 52, 55, 62, 64, 69, 76, 79, 81, 94, 97, 103, 109, 113, 119, 132, 135, 139, 154, 160, 165, 170, 173, 176, 185, 196, 201, 208, 212, 215, 220, 223, 225, 234, 239, 245, 248, 253, 265, 270, 277

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 01 2009

Keywords

• nonn

Comments

The asymptotic density of this sequence is 1/6 (by Dirichlet's theorem). - Amiram Eldar, Mar 02 2021

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000040, A000720, A061240, A093012.

Programs

Maple

for n from 1 to 300 do p := ithprime(n) ; if (p mod 9 ) = 5 then printf("%d,",n) ; fi; od: # R. J. Mathar, Aug 01 2009
A163595 := proc(n) option remember ; local a; if n = 1 then 3 ; else for a from procname(n-1)+1 do if ithprime(a) mod 9 = 5 then return(a) ; fi; end do: end if; end proc: seq(A163595(n),n=1..100) ; # R. J. Mathar, Oct 10 2009

Mathematica

Select[Range[300],Mod[Prime[#],9]==5&]  (* Harvey P. Dale, Apr 25 2011 *)

Formula

A000040(a(n)) = A061240(n).

a(n) = A000720(A061240(n)).