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

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

Author

Parthasarathy Nambi, Feb 20 2005

Keywords

• nonn
• base
• easy

Comments

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)

Examples

			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.
		

Links

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

Crossrefs

Cf. A157772, A102248, A159942, A102611.

Programs

Magma

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

Mathematica

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

PARI

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

Extensions

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