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A097326 Largest integer m such that m*n has the same decimal digit length as n. 2

%I #16 Oct 06 2021 02:46:23

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

%C 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 Michael De Vlieger, <a href="/A097326/b097326.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A097327(n) - 1.

%F a(n) = floor(10^A055642(n) - 1). - _Michael S. Branicky_, Oct 05 2021

%e a(12)=8 as 12 and 8*12=96 both have two decimal digits while 9*12=108 has three.

%t limn[n_]:=Module[{k=9,len=IntegerLength[n]},While[IntegerLength[k*n] > len, k--];k]; Array[limn,110] (* _Harvey P. Dale_, Apr 28 2018 *)

%o (Python)

%o def a(n): return (10**len(str(n))-1)//n

%o print([a(n) for n in range(1, 106)]) # _Michael S. Branicky_, Oct 05 2021

%o (PARI) a(n) = my(m=1, sn=#Str(n)); while (#Str(m*n) <= sn, m++); m-1; \\ _Michel Marcus_, Oct 05 2021

%Y Cf. A061601 (analog for decimal m+n), A035327 (analog for binary m+n), A097327.

%Y Cf. A055642.

%K base,easy,nonn

%O 1,1

%A _Rick L. Shepherd_, Aug 04 2004

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Last modified March 28 14:21 EDT 2024. Contains 371254 sequences. (Running on oeis4.)