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Primes in carryless arithmetic mod 10.
9

%I #12 Oct 04 2012 10:29:13

%S 21,23,25,27,29,41,43,45,47,49,51,52,53,54,56,57,58,59,61,63,65,67,69,

%T 81,83,85,87,89,201,209,227,229,241,243,261,263,287,289,403,407,421,

%U 427,443,449,463,469,481,487,551,553,557,559,603,607,623,629,641,647,661,667,683,689,801,809,821,823,847,849,867,869,881,883

%N Primes in carryless arithmetic mod 10.

%C Define the units in carryless arithmetic mod 10 to be the numbers 1, 3, 7 and 9 (these divide any number). A prime is a number N, not a unit, whose only factorizations are of the form N = u * M, where u is a unit.

%C There are two types: e-type primes (A163396) and f-type (A169984).

%H N. J. A. Sloane, <a href="/A169887/b169887.txt">Table of n, a(n) for n = 1..253560</a> (All primes with <= 9 digits. Based on T. D. Noe's b-files for A058943 and A058955.)

%H David Applegate, Marc LeBrun and N. J. A. Sloane, <a href="http://neilsloane.com/doc/carry1.pdf">Carryless Arithmetic (I): The Mod 10 Version</a>.

%H <a href="/index/Ca#CARRYLESS">Index entries for sequences related to carryless arithmetic</a>

%e Examples of nonprimes: 2 = 2*51, 4 = 2*2, 10 = 52*85, 11 = 57*83, 101 = 13*17, 102 = 58 * 254 = 502 * 801, 103 = 53 * 251 = 507 * 809, 107 = 53 * 259 = 507 * 801, 108 = 58 * 256 = 502 * 809, 111 = 227 * 553.

%Y A169887 = A163396 union A169984.

%Y Cf. A004520, A059729, A168294, A168541, A169885, A169886, A169884, A169903 (primitive primes).

%Y Cf. A169962.

%K nonn,base

%O 1,1

%A _David Applegate_, _Marc LeBrun_ and _N. J. A. Sloane_, Jul 06 2010