A102248 -id:A102248 - 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

A102343 Numbers k such that k*10^3 + 777 is prime.

Original entry on oeis.org

1, 2, 11, 19, 22, 26, 41, 43, 44, 47, 50, 53, 65, 67, 68, 71, 76, 79, 80, 83, 94, 97, 107, 110, 113, 115, 122, 124, 125, 131, 134, 136, 137, 145, 146, 152, 155, 158, 167, 169, 170, 173, 176, 181, 184, 199, 202, 211, 212, 226, 229, 232, 233, 250, 253, 254, 268, 272, 274, 281, 284, 286, 292, 295, 298, 299

Offset: 1

Parthasarathy Nambi, Feb 20 2005

From Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 27 2009: (Start)
The sequence is infinite by Dirichlet's theorem about primes in arithmetic progression.
No term of the sequence is of form 3k, because the sum of digits of 10^3*3k + 333 = 3*(10^3 + 259) is divisible by 3, violating the requirement of the definition. (End)

			k=1: 1*10^3 + 777 = 1777 is prime, hence 1 is in the sequence.
k=50: 50*10^3 + 777 = 50777 is prime, hence 50 is in the sequence.
k=97: 97*10^3 + 777 = 97777 is prime, hence 97 is in the sequence.

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

Cf. A157772, A102248, A159942, A102611.

[ n: n in [0..300] | IsPrime(n*10^3+777) ];

Select[Range[300],PrimeQ[1000#+777]&] (* Harvey P. Dale, Jun 06 2022 *)

is(n)=isprime(n*10^3+777) \\ Charles R Greathouse IV, Jun 13 2017

Extended by Ulrich Krug (leuchtfeuer37(AT)gmx.de), Apr 27 2009
Edited by R. J. Mathar, Apr 30 2009
More terms from Vincenzo Librandi, May 01 2009

A159942 Duplicate of A102339.

Original entry on oeis.org

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

Offset: 1

dead

Cf. A157772, A102248.

A102372 Numbers k such that k11111 is prime.

Original entry on oeis.org

3, 5, 6, 9, 20, 24, 26, 39, 42, 48, 60, 65, 68, 83, 84, 93, 95, 108, 119, 126, 132, 146, 167, 179, 182, 189, 203, 206, 213, 224, 227, 230, 233, 234, 249, 258, 269, 270, 272, 291, 296, 305, 315, 324, 329, 336, 341, 345, 347, 348, 363, 368, 377, 384, 387, 392, 402, 422, 423, 438, 440, 450, 455, 458

Offset: 1

Parthasarathy Nambi, Feb 22 2005

			If k=3, then k11111 = 311111 (prime).
If k=60, then k11111 = 6011111 (prime).
If k=126, then k11111 = 12611111 (prime).

Cf. A101471, A102248, A102249.

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

Select[Range[500],PrimeQ[100000#+11111]&] (* Harvey P. Dale, Jan 15 2013 *)

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

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A102343 Numbers k such that k*10^3 + 777 is prime.

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A159942 Duplicate of A102339.

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A102372 Numbers k such that k11111 is prime.

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