A097327 -id:A097327 - cp's OEIS frontend

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

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, 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, 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

Offset: 1

Rick L. Shepherd, Aug 04 2004

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).

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

Michael De Vlieger, Table of n, a(n) for n = 1..10000

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

Cf. A055642.

limn[n_]:=Module[{k=9,len=IntegerLength[n]},While[IntegerLength[k*n] > len, k--];k]; Array[limn,110] (* Harvey P. Dale, Apr 28 2018 *)
Table[Ceiling[10^IntegerLength[n]/n] - 1, {n, 100}] (* Paolo Xausa, Nov 06 2024 *)

a(n) = my(m=1, sn=#Str(n)); while (#Str(m*n) <= sn, m++); m-1; \\ Michel Marcus, Oct 05 2021

def a(n): return (10**len(str(n))-1)//n
print([a(n) for n in range(1, 106)]) # Michael S. Branicky, Oct 05 2021

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

a(n) = floor((10^A055642(n) - 1)/n). - Michael S. Branicky, Oct 05 2021

A377565 a(n) is the least multiple of n with more decimal digits than n.

Original entry on oeis.org

10, 10, 12, 12, 10, 12, 14, 16, 18, 100, 110, 108, 104, 112, 105, 112, 102, 108, 114, 100, 105, 110, 115, 120, 100, 104, 108, 112, 116, 120, 124, 128, 132, 102, 105, 108, 111, 114, 117, 120, 123, 126, 129, 132, 135, 138, 141, 144, 147, 100, 102, 104, 106, 108

Offset: 1

Rémy Sigrist, Nov 01 2024

			For n = 42: 42 and 2*42 have the same number of digits, while 3*42 has more digits, so a(42) = 3*42 = 126.

Rémy Sigrist, Table of n, a(n) for n = 1..9999

Cf. A055642, A097327, A109940.

Table[n*Ceiling[10^IntegerLength[n]/n], {n, 120}] (* Michael De Vlieger, Nov 02 2024 *)

PARI
```
a(n) = n * ceil(10^#digits(n) / n)
```

def A377565(n): return n-1+10**(l:=len(str(n)))-(pow(10,l,n)-1)%n # Chai Wah Wu, Nov 02 2024

a(n) = n * A097327(n).

cp's OEIS Frontend

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

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