A061238 Prime numbers == 2 (mod 9).

2, 11, 29, 47, 83, 101, 137, 173, 191, 227, 263, 281, 317, 353, 389, 443, 461, 479, 569, 587, 641, 659, 677, 821, 839, 857, 911, 929, 947, 983, 1019, 1091, 1109, 1163, 1181, 1217, 1289, 1307, 1361, 1433, 1451, 1487, 1523, 1559, 1613, 1667, 1721, 1811, 1847

Offset: 1

Author

Amarnath Murthy, Apr 23 2001

Keywords

• nonn
• easy

Comments

A010888(a(n)) = 2. - Reinhard Zumkeller, Feb 25 2005

Except for the first term "2", all current prime numbers are of the form: 18*n-7. - Vladimir Joseph Stephan Orlovsky, Jul 13 2011

Links

• Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A061237..A061242.

Programs

Magma

[ p: p in PrimesUpTo(2000) | p mod 9 in {2} ]; // Vincenzo Librandi, Dec 25 2010

Mathematica

Select[ Range[ 2000 ], PrimeQ[ # ] && Mod[ #, 9 ] == 2 & ]
Join[{2}, Select[Range[11, 5000, 18], PrimeQ]] (* Vladimir Joseph Stephan Orlovsky, Jul 13 2011 *) (* ~30 times faster *)

PARI

select(n->n%9==2, primes(400)) \\ Charles R Greathouse IV, May 27 2014

Formula

a(n) ~ 6n log n. - Charles R Greathouse IV, May 14 2025

Extensions

More terms from Robert G. Wilson v, May 10 2001