A029747 Numbers of the form 2^k times 1, 3 or 5.

1, 2, 3, 4, 5, 6, 8, 10, 12, 16, 20, 24, 32, 40, 48, 64, 80, 96, 128, 160, 192, 256, 320, 384, 512, 640, 768, 1024, 1280, 1536, 2048, 2560, 3072, 4096, 5120, 6144, 8192, 10240, 12288, 16384, 20480, 24576, 32768, 40960, 49152, 65536, 81920, 98304, 131072, 163840, 196608

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Fixed points of the Doudna sequence: A005940(a(n)) = A005941(a(n)) = a(n). - Reinhard Zumkeller, Aug 23 2006

Subsequence of A103969. - R. J. Mathar, Mar 06 2010

Question: Is there a simple proof that A005940(c) = c would never allow an odd composite c as a solution? See also my comments in A163511 and in A335431 concerning similar problems, also A364551 and A364576. - Antti Karttunen, Jul 28 & Aug 11 2023

Examples

			128 = 2^7 * 1 is in the sequence as well as 160 = 2^5 * 5. - _David A. Corneth_, Sep 18 2020
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..9963 (terms <= 10^1000)
• Index entries for linear recurrences with constant coefficients, signature (0,0,2).

Crossrefs

Cf. A122132, A000079, A007283, A020714, A130793.

Cf. A005940, A005941, A163511, A335431, A364499, A364551, A364576.

Subsequence of the following sequences: A103969, A253789, A364541, A364542, A364544, A364546, A364548, A364550, A364560, A364565.

Even terms form a subsequence of A320674.

Programs

Mathematica

m = 200000; Select[Union @ Flatten @ Outer[Times, {1, 3, 5}, 2^Range[0, Floor[Log2[m]]]], # < m &] (* Amiram Eldar, Oct 15 2020 *)

PARI

is(n) = n>>valuation(n, 2) <= 5 \\ David A. Corneth, Sep 18 2020

Python

def A029747(n):
    if n<3: return n
    a, b = divmod(n,3)
    return 1<Chai Wah Wu, Apr 02 2025

Formula

a(n) = if n < 6 then n else 2*a(n-3). - Reinhard Zumkeller, Aug 23 2006

G.f.: (1+x+x^2)^2/(1-2*x^3). - R. J. Mathar, Mar 06 2010

Sum_{n>=1} 1/a(n) = 46/15. - Amiram Eldar, Oct 15 2020

Extensions

Edited by David A. Corneth and Peter Munn, Sep 18 2020