A097327 - OEIS

%I #21 Nov 02 2024 18:00:01

%S 10,5,4,3,2,2,2,2,2,10,10,9,8,8,7,7,6,6,6,5,5,5,5,5,4,4,4,4,4,4,4,4,4,

%T 3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,

%U 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,10,10,10

%N Least positive integer m such that m*n has greater decimal digit length than n.

%C For any positive base B >= 2 the corresponding sequence contains only terms from 2 to B inclusive so the corresponding sequence for binary is all 2s (A007395).

%H Michael S. Branicky, <a href="/A097327/b097327.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A097326(n) + 1.

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

%e a(12) = 9 since 12 has two decimal digits and 9*12 = 108 has three (but 8*12 = 96 has only two).

%t Table[Ceiling[10^IntegerLength[n]/n], {n, 100}] (* _Paolo Xausa_, Nov 02 2024 *)

%o (Python)

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

%o print([a(n) for n in range(1, 103)]) # _Michael S. Branicky_, Oct 05 2021

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

%Y Cf. A089186 (analog for decimal m+n), A080079 (analog for binary m+n), A097326.

%Y Cf. A055642.

%K base,easy,nonn

%O 1,1

%A _Rick L. Shepherd_, Aug 04 2004