cp's OEIS Frontend

A097326 Largest integer m such that m*n has the same decimal digit length as n.

%I A097326 #24 Nov 07 2024 09:53:30
%S A097326 9,4,3,2,1,1,1,1,1,9,9,8,7,7,6,6,5,5,5,4,4,4,4,4,3,3,3,3,3,3,3,3,3,2,
%T A097326 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A097326 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,9,9,9,9,9,9
%N A097326 Largest integer m such that m*n has the same decimal digit length as n.
%C A097326 For any positive base B >= 2 the corresponding sequence contains only terms from 1 to B-1 inclusive so the corresponding sequence for binary is all 1's (A000012).
%H A097326 Michael De Vlieger, <a href="/A097326/b097326.txt">Table of n, a(n) for n = 1..10000</a>
%F A097326 a(n) = A097327(n) - 1.
%F A097326 a(n) = floor((10^A055642(n) - 1)/n). - _Michael S. Branicky_, Oct 05 2021
%e A097326 a(12)=8 as 12 and 8*12=96 both have two decimal digits while 9*12=108 has three.
%t A097326 limn[n_]:=Module[{k=9,len=IntegerLength[n]},While[IntegerLength[k*n] > len, k--];k]; Array[limn,110] (* _Harvey P. Dale_, Apr 28 2018 *)
%t A097326 Table[Ceiling[10^IntegerLength[n]/n] - 1, {n, 100}] (* _Paolo Xausa_, Nov 06 2024 *)
%o A097326 (Python)
%o A097326 def a(n): return (10**len(str(n))-1)//n
%o A097326 print([a(n) for n in range(1, 106)]) # _Michael S. Branicky_, Oct 05 2021
%o A097326 (PARI) a(n) = my(m=1, sn=#Str(n)); while (#Str(m*n) <= sn, m++); m-1; \\ _Michel Marcus_, Oct 05 2021
%Y A097326 Cf. A061601 (analog for decimal m+n), A035327 (analog for binary m+n), A097327.
%Y A097326 Cf. A055642.
%K A097326 base,easy,nonn
%O A097326 1,1
%A A097326 _Rick L. Shepherd_, Aug 04 2004