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
KEYWORD
nonn
AUTHOR
Parthasarathy Nambi, Feb 20 2005
STATUS
approved