A056955 Euclid set of class 2 and modulus 3.

5, 8, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, 107, 113, 131, 137, 149, 167, 173, 179, 191, 197, 227, 233, 239, 251, 257, 263, 269, 281, 293, 311, 317, 347, 353, 359, 383, 389, 401, 419, 431, 443, 449, 461, 467, 479, 491, 503, 509, 521, 557, 563, 569

Offset

1,1

Comments

For c<m, (m,c)=1, the Euclid(c, m) set is obtained by deleting from the set of numbers c+m*k, for k>0, every term which has a common factor with a smaller term. See Link for more details.

Essentially the same as A003627, which drops the 8 for 2. - Charles R Greathouse IV, Nov 21 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Andrea Ercolino, XGC - An extension of the Goldbach Conjecture

Example

The Euclid(2,3) set is constructed by starting from the set of numbers of the form 2+3*k for k>0, i.e., 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35,... and deleting every term which has a common factor with a previous one, like 14, 20, 26, 32, 35,... and so on.

Mathematica

eu[c_, m_, n_] := Block[{v, k=1, p=1}, Table[ While[GCD[v = c + m*k, p] > 1, k++]; p *= v; v, {n}]]; eu[2, 3, 55] (* Giovanni Resta, Mar 14 2014 *)

Prog

(PARI) is(n)=n%3==2 && ((isprime(n) && n>2) || n==8) \\ Charles R Greathouse IV, Nov 21 2014

Crossrefs

Sequence in context: A314393 A162939 A314394 * A023381 A314395 A314396

Adjacent sequences: A056952 A056953 A056954 * A056956 A056957 A056958

Keyword

nonn,easy

Author

Andrea Ercolino (aercolino(AT)yahoo.com)

Extensions

Edited by Giovanni Resta, Mar 14 2014

Status

approved