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A102339 Numbers k such that k*10^3 + 333 is prime. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 9 00:09 EDT 2021. Contains 343685 sequences. (Running on oeis4.)