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A056955 Euclid set of class 2 and modulus 3. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 6 04:42 EST 2021. Contains 341842 sequences. (Running on oeis4.)