A122098 - OEIS

%I #18 Nov 06 2021 11:05:23

%S 11,6,11,6,3,6,11,6,11,11,101,26,101,51,21,26,101,51,101,6,101,51,101,

%T 26,5,51,101,26,101,11,101,26,101,51,21,26,101,51,101,6,101,51,101,26,

%U 21,51,101,26,101,3,101,26,101,51,21,26,101,51,101,6,101,51,101,26,21

%N Smallest number, different from 1, which when multiplied by "n" produces a number with "n" as its rightmost digits.

%C All prime numbers p > 5 must be multiplied by 1+10^k, where k is the number of digits of p. The result is p U p. - _Paolo P. Lava_, Apr 11 2008

%D Giorgio Balzarotti and Paolo P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 100.

%H Harvey P. Dale, <a href="/A122098/b122098.txt">Table of n, a(n) for n = 1..1000</a>

%e a(8) = 6 because 8*6 = 48 and 6 is the minimum number that multiplied by 8 gives a number ending in 8.

%e a(12) = 26 because 12*26 = 312 and 26 is the minimum number that multiplied by 12 gives a number ending in 12.

%p P:=proc(n) local a,b,i,j; print(11); for i from 2 by 1 to n do b:=trunc(evalf(log10(i)))+1; for j from 2 by 1 to n do a:=i*j; if i=a-trunc(a/10^b)*10^b then print(j); break; fi; od; od; end: P(101); # _Paolo P. Lava_, Apr 11 2008

%t snrd[n_]:=Module[{k=2},While[Mod[k*n,10^IntegerLength[n]]!=n,k++];k]; Array[ snrd,70] (* _Harvey P. Dale_, Apr 08 2019 *)

%o (Python)

%o def a(n):

%o     kn, s = 2*n, str(n)

%o     while not str(kn).endswith(s): kn += n

%o     return kn//n

%o print([a(n) for n in range(1, 66)]) # _Michael S. Branicky_, Nov 06 2021

%Y Cf. A080501.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Oct 18 2006