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%I #58 Jan 17 2024 09:10:52
%S 1,2,3,4,5,6,8,10,12,16,20,24,32,40,48,64,80,96,128,160,192,256,320,
%T 384,512,640,768,1024,1280,1536,2048,2560,3072,4096,5120,6144,8192,
%U 10240,12288,16384,20480,24576,32768,40960,49152,65536,81920,98304,131072,163840,196608
%N Numbers of the form 2^k times 1, 3 or 5.
%C Fixed points of the Doudna sequence: A005940(a(n)) = A005941(a(n)) = a(n). - _Reinhard Zumkeller_, Aug 23 2006
%C Subsequence of A103969. - _R. J. Mathar_, Mar 06 2010
%C 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
%H David A. Corneth, <a href="/A029747/b029747.txt">Table of n, a(n) for n = 1..9963</a> (terms <= 10^1000)
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,2).
%F a(n) = if n < 6 then n else 2*a(n-3). - _Reinhard Zumkeller_, Aug 23 2006
%F G.f.: (1+x+x^2)^2/(1-2*x^3). - _R. J. Mathar_, Mar 06 2010
%F Sum_{n>=1} 1/a(n) = 46/15. - _Amiram Eldar_, Oct 15 2020
%e 128 = 2^7 * 1 is in the sequence as well as 160 = 2^5 * 5. - _David A. Corneth_, Sep 18 2020
%t m = 200000; Select[Union @ Flatten @ Outer[Times, {1, 3, 5}, 2^Range[0, Floor[Log2[m]]]], # < m &] (* _Amiram Eldar_, Oct 15 2020 *)
%o (PARI) is(n) = n>>valuation(n, 2) <= 5 \\ _David A. Corneth_, Sep 18 2020
%Y Cf. A122132, A000079, A007283, A020714, A130793.
%Y Cf. A005940, A005941, A163511, A335431, A364499, A364551, A364576.
%Y Subsequence of the following sequences: A103969, A253789, A364541, A364542, A364544, A364546, A364548, A364550, A364560, A364565.
%Y Even terms form a subsequence of A320674.
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_.
%E Edited by _David A. Corneth_ and _Peter Munn_, Sep 18 2020
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