cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

Original entry on oeis.org

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
Offset: 1

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Author

Anthony Sand, Jun 12 2014

Keywords

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.

Examples

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

Crossrefs

Programs

  • Mathematica
    NestList[FromDigits@ DeleteCases[IntegerDigits[3 #], ?(# == 0 &)] &, 1, 38] (* _Michael De Vlieger, Jun 27 2020 *)
  • 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

Formula

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

Extensions

Edited: Name, comments and formula reformulated. - Wolfdieter Lang, Jul 13 2014