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%I A169911 #13 Jul 12 2013 08:46:41
%S A169911 3,6,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,31,
%T A169911 32,34,35,37,38,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,
%U A169911 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 A169911 Primes in carryless digital root arithmetic in base 10.
%C A169911 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 A169911 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 A169911 All numbers of the form 100...01 (with k >= 0 zeros) are prime, so there are infinitely many primes.
%H A169911 N. J. A. Sloane, <a href="/A169911/b169911.txt">Table of n, a(n) for n = 1..458</a>
%H A169911 <a href="/index/Ca#CARRYLESS">Index entries for sequences related to carryless arithmetic</a>
%e A169911 96 has a representation 31*6 and is not in the sequence.
%p A169911 # carryLmult implemented in A169908
%p A169911 isA169911 := proc(n)
%p A169911     local a,b,un ;
%p A169911     un := {1,2,4,5,7,8} ;
%p A169911     for a from 1 to n do
%p A169911     for b from 1 to a do
%p A169911         if a in un or b in un then
%p A169911             ;
%p A169911         else
%p A169911             if carryLmult(a,b) = n then
%p A169911                 return false;
%p A169911             end if;
%p A169911         end if;
%p A169911     end do:
%p A169911     end do:
%p A169911     if n in un then
%p A169911         false ;
%p A169911     else
%p A169911         true;
%p A169911     end if;
%p A169911 end proc:
%p A169911   e := 1:
%p A169911 for n from 1 do
%p A169911     if isA169911(n) then
%p A169911         printf("%d %d\n",e,n) ;
%p A169911         e := e+1 ;
%p A169911     end if;
%p A169911 end do: # _R. J. Mathar_, Jul 12 2013
%K A169911 nonn,base
%O A169911 1,1
%A A169911 _David Applegate_, _Marc LeBrun_ and _N. J. A. Sloane_, Jul 11 2010

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