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A122098 Smallest number, different from 1, which when multiplied by "n" produces a number with "n" as its rightmost digits.

%I A122098 #18 Nov 06 2021 11:05:23
%S A122098 11,6,11,6,3,6,11,6,11,11,101,26,101,51,21,26,101,51,101,6,101,51,101,
%T A122098 26,5,51,101,26,101,11,101,26,101,51,21,26,101,51,101,6,101,51,101,26,
%U A122098 21,51,101,26,101,3,101,26,101,51,21,26,101,51,101,6,101,51,101,26,21
%N A122098 Smallest number, different from 1, which when multiplied by "n" produces a number with "n" as its rightmost digits.
%C A122098 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 A122098 Giorgio Balzarotti and Paolo P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 100.
%H A122098 Harvey P. Dale, <a href="/A122098/b122098.txt">Table of n, a(n) for n = 1..1000</a>
%e A122098 a(8) = 6 because 8*6 = 48 and 6 is the minimum number that multiplied by 8 gives a number ending in 8.
%e A122098 a(12) = 26 because 12*26 = 312 and 26 is the minimum number that multiplied by 12 gives a number ending in 12.
%p A122098 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 A122098 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 A122098 (Python)
%o A122098 def a(n):
%o A122098     kn, s = 2*n, str(n)
%o A122098     while not str(kn).endswith(s): kn += n
%o A122098     return kn//n
%o A122098 print([a(n) for n in range(1, 66)]) # _Michael S. Branicky_, Nov 06 2021
%Y A122098 Cf. A080501.
%K A122098 nonn,base
%O A122098 1,1
%A A122098 _Paolo P. Lava_ and _Giorgio Balzarotti_, Oct 18 2006