%I #13 Jul 12 2013 08:46:41

%S 3,6,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,31,

%T 32,34,35,37,38,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,

%U 58,59,61,62,64,65,67,68,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87

%N Primes in carryless digital root arithmetic in base 10.

%C Addition and multiplication are the same as in school, that is, done in base 10, except that there are no carries and when individual digits are added or multiplied the result is replaced by its digital root (A010888).

%C The units are {1,2,4,5,7,8}. A prime is a number N whose only factorizations are of the form N = u*M where u is a unit.

%C All numbers of the form 100...01 (with k >= 0 zeros) are prime, so there are infinitely many primes.

%H N. J. A. Sloane, <a href="/A169911/b169911.txt">Table of n, a(n) for n = 1..458</a>

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

%e 96 has a representation 31*6 and is not in the sequence.

%p # carryLmult implemented in A169908

%p isA169911 := proc(n)

%p local a,b,un ;

%p un := {1,2,4,5,7,8} ;

%p for a from 1 to n do

%p for b from 1 to a do

%p if a in un or b in un then

%p ;

%p else

%p if carryLmult(a,b) = n then

%p return false;

%p end if;

%p end if;

%p end do:

%p end do:

%p if n in un then

%p false ;

%p else

%p true;

%p end if;

%p end proc:

%p e := 1:

%p for n from 1 do

%p if isA169911(n) then

%p printf("%d %d\n",e,n) ;

%p e := e+1 ;

%p end if;

%p end do: # _R. J. Mathar_, Jul 12 2013

%K nonn,base

%O 1,1

%A _David Applegate_, _Marc LeBrun_ and _N. J. A. Sloane_, Jul 11 2010