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

1,1

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

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Dirichlet's Theorem

Example

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).

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 *)

Prog

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

Crossrefs

Cf. A101472, A157772, A102248.

Sequence in context: A018270 A080180 A159942 * A172410 A266594 A103871

Adjacent sequences: A102336 A102337 A102338 * A102340 A102341 A102342

Keyword

nonn

Author

Parthasarathy Nambi, Feb 20 2005

Status

approved