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A073912 Smallest number m such that m and the product of digits of m are both divisible by 8n, or 0 if no such number exists. 4

%I #14 Jun 21 2018 03:23:17

%S 8,48,168,288,0,384,728,448,1368,0,0,384,0,784,0,2688,0,3168,0,0,7896,

%T 0,0,2688,0,0,4968,12768,0,0,0,4864,0,0,0,4896,0,0,0,0,0,8736,0,0,0,0,

%U 0,2688,74872,0,0,0,0,22896,0,14784,0,0,0,0,0,0,33768,14848,0,0,0,0,0

%N Smallest number m such that m and the product of digits of m are both divisible by 8n, or 0 if no such number exists.

%C Here 0 is regarded as not divisible by any number.

%C a(n) = 0 if 10 divides n or n contains a prime divisor > 9. - _Sascha Kurz_, Aug 23 2002

%F a(n) = A085124(8*n). - _R. J. Mathar_, Jun 21 2018

%p f := 8:for i from 1 to 400 do b := ifactors(f*i)[2]: if b[nops(b)][1]>9 or (f*i mod 10) =0 then a[i] := 0:else j := 0:while true do j := j+f*i:c := convert(j,base,10): d := product(c[k],k=1..nops(c)): if (d mod f*i)=0 and d>0 then a[i] := j:break:fi: od:fi:od:seq(a[k],k=1..400);

%Y Cf. A073906, A085124, A073908, A073909, A073910, A073911.

%K nonn,base

%O 1,1

%A _Amarnath Murthy_, Aug 18 2002

%E More terms from _Sascha Kurz_, Aug 23 2002

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Last modified March 29 11:14 EDT 2024. Contains 371278 sequences. (Running on oeis4.)