cp's OEIS Frontend

A382137 Smallest integer that cannot be converted to a multiple of n by changing at most one of its decimal digit.

%I A382137 #40 Jul 21 2025 08:56:37
%S A382137 545,51,44,31,21,21,22,21,21,11,15,11,11,11,11,11,12,11,11,11,14,11,
%T A382137 11,11,11,11,11,11,11,11,13,11,11,11,11,11,11,11,11,11,12,11,11,11,11,
%U A382137 11,11,11,11,11,12,11,11,11,11,11,11,11,11,11,12,11,11,11,11,11,11,11,11,11,12
%N A382137 Smallest integer that cannot be converted to a multiple of n by changing at most one of its decimal digit.
%C A382137 a(n) is not defined for n<11 since any integer can be converted to a multiple of n by changing its last digit.
%C A382137 For all n, a(n)>=11, since any number <=10 ca be converted to 0 which is a multiple of n.
%C A382137 For n>=42, a(n)=11, except for a(51)=a(61)=a(71)=a(81)=a(91)=12. Especially a(n)=11 for all n>=100 because 11 is the first integer that cannot be converted to 0 or a 3-digit number.
%H A382137 Mickaël Launay, <a href="https://www.lemonde.fr/sciences/article/2025/03/08/le-demon-des-multiples-l-enigme-maths-du-monde-n-48_6577317_1650684.html">Le démon des multiples</a>, L’énigme maths du "Monde" n°48. In French.
%e A382137 For n=12, any number<50 can be converted to a multiple of 12 by changing its last digit. Since a) there is no multiple of 12 between 50 and 59 so changing the last digit is useless, b) 50 can be converted to 60=5*12 and c) changing the "5" of 51 gives only odd (non multiples of 12) numbers, then a(12)=51.
%o A382137 (Python)
%o A382137 import math
%o A382137 def test(N,M):
%o A382137    t = True
%o A382137    for i in range(0,math.floor(math.log(N,10))+1):
%o A382137       for j in range(0,10): t = t and ((N+(j-N // 10**i % 10)*10**i)%M != 0)
%o A382137    return t
%o A382137 for M in range(11,100):
%o A382137    N = 1
%o A382137    while (not test(N,M)): N += 1
%o A382137    print(N, end=', ')
%Y A382137 Cf. A353023, A192545.
%K A382137 nonn,base
%O A382137 11,1
%A A382137 _Mickaël Launay_, Mar 27 2025