%I A062400
%S A062400 2,2,6,4,80,6,46802,8,468,80,68024,24,468,46802,4680,80,68,468,6802,80,
%T A062400 80246802468,68024,46,24,0,468,680246802,80246802468,680246802468,4680,
%U A062400 24680246802468,0,680246802468024,68,802468024680,468,24680246802468,6802
%N A062400 Smallest multiple of n with property that digits are even and each digit 
               is two more (mod 10) than the previous digit; or 0 if no such multiple 
               exists.
%C A062400 If a(n) = 0, a(n*k) = 0 for any positive k. - Franklin T. Adams-Watters 
               (FrankTAW(AT)Netscape.net), Nov 03 2009
%C A062400 25 is impossible; its multiples end either with the digits 00 or 50.
%C A062400 Multiples of 16 except 16 and 80 are impossible. Of the 625 multiples 
               of of 16 mod 10000, none are 246, 2468, 4680, 6802, or 8024. That 
               leaves only 80 as a possible value for multiples of 16. It appears 
               that the multiples of 16 and 25 are the only numbers for which a(n) 
               = 0 - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Nov 03 
               2009
%H A062400 Franklin T. Adams-Watters, <a href="b062400.txt">Table of n, a(n) for 
               n = 1..1000.</a>
%e A062400 a(7) = 7*6686 = 46802 and this number has increasing larger even digits 
               (mod 10). a(12) = 24 = 12*2 has increasing even digits.
%t A062400 f[n_] := Block[{x = 0, a = IntegerDigits[n], i = 1}, l =Length[a]; While 
               < l, If[ Mod[ a[[i]] + 2, 10] != a + 1]], x = 1]; i++ ]; Return[x]]; 
               Dock = n; While[ Union[ even[ IntegerDigits[k]]] != {True} || Fmk] 
               == 1, k += n]; Print[k], {n, 1, 20}]
%o A062400 (PARI) evenincr(n)=local(d,r);d=n%4*2+2;n\=4;r=0;for(k=0,n,r=r*10+(d+2*k)%10);
               r
%o A062400 a(n)=if(n%25==0|(n%16==0&80%n!=0),0,k=0;while(evenincr(k)%n!=0,k++);evenincr(k))
%o A062400 /* This program will loop if the conjecture above is incorrect. */
%Y A062400 Sequence in context: A062885 A062293 A054516 this_sequence A064766 A121178 
               A019749
%Y A062400 Adjacent sequences: A062397 A062398 A062399 this_sequence A062401 A062402 
               A062403
%K A062400 nonn,base,easy
%O A062400 1,1
%A A062400 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Jun 28 2001
%E A062400 Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 22 
               2002
%E A062400 Edited and extended by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), 
               Nov 03 2009