A243845 - OEIS

%I #28 Jun 29 2020 02:26:31

%S 1,3,9,27,81,243,729,2187,6561,19683,5949,17847,53541,16623,49869,

%T 14967,4491,13473,4419,13257,39771,119313,357939,173817,521451,

%U 1564353,469359,14877,44631,133893,41679,12537,37611,112833,338499,115497,346491,139473,418419

%N Numbers generated by recursive procedure a(n) = nozero(a(n-1) * 3), in which the function nozero(x) removes all zeros from x, starting with a(1) = 1.

%C Numbers in the following sequence: Let a(1) = 1, then begin the recursive sequence a(n) = nozero(a(n-1) * 3), where the function nozero(x) removes all zeros from x.

%C The sequence returns standard powers of 3 until step 11, where a(11) = nozero(19683 * 3) = nozero(59049) = 5949.

%C At step 28, a(28) = nozero(469359 * 3) = nozero(1408077) = 14877. At step 108, a(108) = nozero(4959 * 3) = 14877. Therefore a(28) = a(108) and the sequence repeats. Because this is the first instance where a member of this sequence is repeated one has a(n + L) = a(n) for n >= 28 with the primitive (least) period length L = 108 - 28 = 80.

%H Anthony Sand, <a href="/A243845/b243845.txt">Table of n, a(n) for n = 1..108</a>

%H <a href="/index/Rec#order_80">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

%F a(n) = A004719(a(n-1) * 3) for n>1, a(1) = 1.

%e a(2) = nozero(3*a(1)) = nozero(3) = 3.

%t NestList[FromDigits@ DeleteCases[IntegerDigits[3 #], _?(# == 0 &)] &, 1, 38] (* _Michael De Vlieger_, Jun 27 2020 *)

%o (Sage)

%o L=[1]

%o for i in [1..108]:

%o     T=(3*L[i-1]).digits(base=10)

%o     TT=filter(lambda a: a != 0, T)

%o     L.append(sum(TTi*10^i for i, TTi in enumerate(TT)))

%o L # - _Tom Edgar_, Jun 17 2014

%Y Cf. A000244, A004719, A242350, A243846.

%K nonn,base

%O 1,2

%A _Anthony Sand_, Jun 12 2014

%E Edited: Name, comments and formula reformulated. - _Wolfdieter Lang_, Jul 13 2014