cp's OEIS Frontend

A097327 Least positive integer m such that m*n has greater decimal digit length than n.

%I A097327 #21 Nov 02 2024 18:00:01
%S A097327 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 A097327 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 A097327 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 A097327 Least positive integer m such that m*n has greater decimal digit length than n.
%C A097327 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 A097327 Michael S. Branicky, <a href="/A097327/b097327.txt">Table of n, a(n) for n = 1..10000</a>
%F A097327 a(n) = A097326(n) + 1.
%F A097327 a(n) = ceiling(10^A055642(n)/n). - _Michael S. Branicky_, Oct 05 2021
%e A097327 a(12) = 9 since 12 has two decimal digits and 9*12 = 108 has three (but 8*12 = 96 has only two).
%t A097327 Table[Ceiling[10^IntegerLength[n]/n], {n, 100}] (* _Paolo Xausa_, Nov 02 2024 *)
%o A097327 (Python)
%o A097327 def a(n): return (10**len(str(n))-1)//n + 1
%o A097327 print([a(n) for n in range(1, 103)]) # _Michael S. Branicky_, Oct 05 2021
%o A097327 (PARI) a(n) = my(m=1, sn=#Str(n)); while (#Str(m*n) <= sn, m++); m; \\ _Michel Marcus_, Oct 05 2021
%Y A097327 Cf. A089186 (analog for decimal m+n), A080079 (analog for binary m+n), A097326.
%Y A097327 Cf. A055642.
%K A097327 base,easy,nonn
%O A097327 1,1
%A A097327 _Rick L. Shepherd_, Aug 04 2004