A030431 Primes of form 10n+3.

3, 13, 23, 43, 53, 73, 83, 103, 113, 163, 173, 193, 223, 233, 263, 283, 293, 313, 353, 373, 383, 433, 443, 463, 503, 523, 563, 593, 613, 643, 653, 673, 683, 733, 743, 773, 823, 853, 863, 883, 953, 983, 1013, 1033, 1063, 1093, 1103, 1123, 1153, 1163, 1193

Offset: 1

Author

Warut Roonguthai

Keywords

• nonn

Comments

Also primes of form 5n+3.

Union of A132233, A132235, {3}. - Ray Chandler, Apr 07 2009

Primes p such that arithmetic mean of divisors of p^4 is an integer. There are 2 such sequences of primes, this one and A030430. - Ctibor O. Zizka, Oct 20 2009

5 is not quadratic residue of primes of this form. - Vincenzo Librandi, Jun 25 2014

Intersection of A000040 and A017305. - Iain Fox, Dec 30 2017

Links

• Michael B. Porter, Table of n, a(n) for n = 1..100000
• A. Granville and G. Martin, Prime number races, arXiv:math/0408319 [math.NT], 2004.

Crossrefs

Cf. A045414, A049508, A053179, A102338.

Programs

Mathematica

Select[Prime@Range[200], Mod[ #, 10] == 3 &] (* Ray Chandler, Nov 07 2006 *)
Select[10 Range[0, 150] + 3, PrimeQ]  (* Harvey P. Dale, Apr 06 2011 *)

PARI

select(n->n%10==3, primes(500)) \\ Charles R Greathouse IV, Apr 29 2015

Formula

a(n) = 10*A102338(n) + 3.

Extensions

Extended by Ray Chandler, Nov 07 2006