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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
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
Sequence in context: A300148 A190128 A216097 * A354269 A140429 A141413
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.)