|
%I #20 Oct 13 2018 12:58:52
%S 1,12,30,46,83,1099,1571,17902874277
%N Smallest positive integer with multiplicative persistence n in base 12.
%C The sequence in base 12 is 1, 10, 26, 3X, 6E, 777, XXE, 3577777799, where X is 10 and E is 11. I have searched numbers up to 24 digits in base 12 excluding any numbers that might contain the digit 1 or any combination of digits that might multiply to 0 mod 12. The numbers also had digits in nondecreasing order, so that XXE would be tested but, for example, EXX would not.
%e a(0)=1 since 1 is the smallest positive integer for which no multiplication takes place. [Edited by _A.H.M. Smeets_, Sep 16 2018]
%e a(6)=1571 since 1571, 1100, 392, 128, 80, 48, 0 is the chain with six multiplications. In base 12, XXE, 778, 288, X8, 68, 40, 0.
%p Maple program available upon request.
%t With[{s = Array[-1 + Length@ FixedPointList[Times @@ IntegerDigits[#, 12] &, #] &, 1600]}, Array[FirstPosition[s, #][[1]] &, Max@ s]] (* _Michael De Vlieger_, Sep 18 2018 *)
%Y Cf. A003001, A031346, A046510, A064867, A064868, A064869, A064870, A064871, A064872.
%K more,nonn,base
%O 0,2
%A _Walter Kehowski_, Jan 04 2007
|
