A101472 -id:A101472 - cp's OEIS frontend

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

Parthasarathy Nambi, Feb 20 2005

nonn

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

			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).

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

Cf. A101472, A157772, A102248.

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

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

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 *)

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

A102340 Numbers k such that k3333 is prime.

Original entry on oeis.org

2, 10, 14, 31, 32, 34, 35, 49, 52, 73, 74, 79, 80, 92, 95, 97, 113, 116, 118, 125, 127, 128, 134, 136, 139, 142, 148, 149, 155, 160, 169, 172, 178, 185, 196, 205, 211, 217, 224, 227, 238, 245, 251, 260, 262, 263, 265, 272, 281, 283, 284, 287, 296, 298, 304, 305, 311, 322, 323, 325, 326, 335, 343

Offset: 1

Parthasarathy Nambi, Feb 20 2005

			k=2 is in the sequence because  k3333 = 23333 is prime.
k=73 is in the sequence because k3333 = 733333 is prime.
k=125 is in the sequence because k3333 = 1253333 is prime.

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

Cf. A101472.

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

Select[Range[500],PrimeQ[FromDigits[Join[IntegerDigits[#],{3,3,3,3}]]]&] (* Harvey P. Dale, Jun 17 2014 *)
Select[Range[500],PrimeQ[#*10^4+3333]&] (* Harvey P. Dale, Jun 15 2024 *)

A104130 Numbers n such that n33 is prime and n is a multiple of ten.

Original entry on oeis.org

10, 130, 140, 160, 170, 250, 290, 310, 340, 490, 500, 640, 650, 670, 910, 920, 940, 1040, 1060, 1070, 1180, 1190, 1220, 1270, 1280, 1330, 1340, 1360, 1390, 1460, 1490, 1600, 1610, 1670, 1790, 1910, 1960, 1970, 1990, 2000, 2050, 2060, 2140, 2170, 2240, 2440, 2450, 2480, 2510, 2560

Offset: 1

Parthasarathy Nambi, Mar 06 2005

			If t=10, then t33 = 1033 (prime).
If t=170, then t33 = 17033 (prime).
If t=490, then t33 = 49033 (prime).

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Intersection of A008592 and A101472.

Select[10 Range[300],PrimeQ[100#+33]&] (* Harvey P. Dale, Jan 08 2021 *)

for(k=1,230,if(isprime(1000*k+33),print1(10*k,", "))) \\ Hugo Pfoertner, Dec 21 2019

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

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A102340 Numbers k such that k3333 is prime.

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A104130 Numbers n such that n33 is prime and n is a multiple of ten.

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