A073910 - OEIS

A073910

Smallest number m such that m and the product of digits of m are both divisible by 3n, or 0 if no such number exists.

3, 6, 9, 168, 135, 36, 273, 168, 999, 0, 0, 1296, 0, 378, 495, 384, 0, 1296, 0, 0, 1197, 0, 0, 1368, 3525, 0, 2997, 672, 0, 0, 0, 384, 0, 0, 735, 1296, 0, 0, 0, 0, 0, 3276, 0, 0, 3915, 0, 0, 3168, 7497, 0, 0, 0, 0, 5994, 0, 7896, 0, 0, 0, 0, 0, 0, 7938, 2688, 0, 0, 0, 0, 0, 0, 0

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OFFSET

1,1

COMMENTS

Here 0 is regarded as not divisible by any number.

a(n) = 0 if 10 divides 3n or n contains a prime divisor > 9. - Sascha Kurz, Aug 23 2002

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A085124(3*n). - R. J. Mathar, Jun 21 2018

MAPLE

f := 3:for i from 1 to 1000 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..1000);

CROSSREFS

Cf. A073906, A073908, A073909, A073911, A073912, A085124.

Sequence in context: A103978 A289064 A293537 * A115251 A057241 A104617

Adjacent sequences: A073907 A073908 A073909 * A073911 A073912 A073913

KEYWORD

nonn,base

AUTHOR

Amarnath Murthy, Aug 18 2002

EXTENSIONS

More terms from Sascha Kurz, Aug 23 2002

STATUS

approved