A102339 Numbers k such that k*10^3 + 333 is prime.

2, 5, 7, 10, 16, 17, 19, 20, 23, 29, 31, 38, 41, 49, 50, 55, 56, 59, 61, 64, 71, 76, 79, 85, 92, 100, 101, 103, 121, 134, 136, 139, 140, 143, 149, 154, 155, 161, 175, 176, 178, 182, 184, 188, 208, 209, 211, 217, 220, 232, 236, 239, 241, 244, 265, 266, 269, 271, 272, 274, 286, 287, 295, 299, 301, 308

Offset: 1

Author

Parthasarathy Nambi, Feb 20 2005

Keywords

• nonn

Comments

10^3 and 333 are relatively prime, therefore by Dirichlet's theorem there are infinitely many primes in the arithmetic progression n*10^3+333. No term of the sequence is of the form 3*k, because 3*k*10^3+333 = 3*(k*10^3+111) is divisible by 3, violating the requirement of the definition. - Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 27 2009

Examples

			If k=2,  then k*10^3 + 333 =  2333 (prime).
If k=49, then k*10^3 + 333 = 49333 (prime).
If k=92, then k*10^3 + 333 = 92333 (prime).
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Dirichlet's Theorem

Crossrefs

Cf. A101472, A157772, A102248.

Programs

Magma

[ n: n in [1..700] | IsPrime(Seqint([3,3,3] cat Intseq(n))) ]; // Vincenzo Librandi, Feb 04 2011

Magma

[ n: n in [0..320] | IsPrime(n*10^3+333) ]; // Klaus Brockhaus, May 20 2009

Mathematica

Select[Range[400],PrimeQ[FromDigits[Join[IntegerDigits[#],{3,3,3}]]]&] (* Harvey P. Dale, Oct 14 2014 *)
Select[Range[0, 1000], PrimeQ[1000 # + 333] &] (* Vincenzo Librandi, Jan 19 2013 *)

PARI

is(n)=isprime(1000*n+333) \\ Charles R Greathouse IV, Jun 06 2017