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 A243845 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. 3
 1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 5949, 17847, 53541, 16623, 49869, 14967, 4491, 13473, 4419, 13257, 39771, 119313, 357939, 173817, 521451, 1564353, 469359, 14877, 44631, 133893, 41679, 12537, 37611, 112833, 338499, 115497, 346491, 139473, 418419 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. The sequence returns standard powers of 3 until step 11, where a(11) = nozero(19683 * 3) = nozero(59049) = 5949. 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. LINKS Anthony Sand, Table of n, a(n) for n = 1..108 Index entries for linear recurrences with constant coefficients, 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). FORMULA a(n) = A004719(a(n-1) * 3) for n>1, a(1) = 1. EXAMPLE a(2) = nozero(3*a(1)) = nozero(3) = 3. MATHEMATICA NestList[FromDigits@ DeleteCases[IntegerDigits[3 #], _?(# == 0 &)] &, 1, 38] (* Michael De Vlieger, Jun 27 2020 *) PROG (Sage) L=[1] for i in [1..108]: T=(3*L[i-1]).digits(base=10) TT=filter(lambda a: a != 0, T) L.append(sum(TTi*10^i for i, TTi in enumerate(TT))) L # - Tom Edgar, Jun 17 2014 CROSSREFS Cf. A000244, A004719, A242350, A243846. Sequence in context: A300148 A190128 A216097 * A354269 A140429 A141413 Adjacent sequences: A243842 A243843 A243844 * A243846 A243847 A243848 KEYWORD nonn,base AUTHOR Anthony Sand, Jun 12 2014 EXTENSIONS Edited: Name, comments and formula reformulated. - Wolfdieter Lang, Jul 13 2014 STATUS approved

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Last modified July 13 00:23 EDT 2024. Contains 374259 sequences. (Running on oeis4.)