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

1,2

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)

Links

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

Example

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.

Mathematica

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

Prog

(Magma) [ n: n in [0..300] | IsPrime(n*10^3+777) ];
(PARI) is(n)=isprime(n*10^3+777) \\ Charles R Greathouse IV, Jun 13 2017

Crossrefs

Cf. A157772, A102248, A159942, A102611.

Sequence in context: A074926 A352932 A066144 * A023173 A018443 A163058

Adjacent sequences: A102340 A102341 A102342 * A102344 A102345 A102346

Keyword

nonn,base,easy

Author

Parthasarathy Nambi, Feb 20 2005

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

Status

approved