%I #23 Aug 08 2023 11:58:56
%S 2,6,26,126,6251,62500001,6250000000000001,
%T 6250000000000000000000000000001,
%U 62500000000000000000000000000000000000000000000000000000000001
%N Start with the seed a(0)=2. The minimum number, different from 1, that multiplied by 2 (seed) produces a number with 2 as its rightmost digit is a(1)=6. Then 6*2=12. Again, the minimum number that multiplied by 12 produces 12 as its rightmost digits is a(2)=26 (12*26=312). And so on.
%D G. Balzarotti and P. P. Lava, Le sequenze di numeri interi, Hoepli, 2008, p. 99.
%e a(0)=2;
%e a(1)=6 because 2*6 = 12;
%e a(2)=26 because 12*26 = 312;
%e a(3)=126 because 312*126 = 39312;
%e a(4)=6251 because 39312*6251 = 245739312;
%e a(5)=62500001 because 245739312*62500001 = 15358707245739312.
%p P:=proc(q,h) local a,b,k,n; a:=h; b:=ilog10(a)+1; print(h);
%p for k from 1 to 10 do for n from 2 to q do
%p if ((a*n) mod 10^b)=a then print(n); a:=a*n; b:=ilog10(a)+1;
%p break; fi; od; od; end: P(10^9,2);
%o (Python)
%o import math
%o p,n = 2,0
%o while n<10:
%o ndigits, oldp = len(str(p)), p
%o p += math.lcm(p,10**ndigits)
%o print("a(%d) = %d"%(n:=n+1, p//oldp))
%o # _Bert Dobbelaere_, Aug 08 2023
%Y Cf. A123873, A123874, A123875.
%K nonn,base
%O 0,1
%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Oct 16 2006
%E More terms from _Bert Dobbelaere_, Aug 08 2023