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%I #48 Jul 19 2022 05:47:14
%S 1,2,4,5,8,10,16,20,21,32,40,42,64,80,84,85,128,160,168,170,256,320,
%T 336,340,341,512,640,672,680,682,1024,1280,1344,1360,1364,1365,2048,
%U 2560,2688,2720,2728,2730,4096,5120,5376,5440,5456,5460,5461,8192,10240
%N Odd part of a(n) is of form (4^k-1)/3.
%C Also numbers that need at most one (3x+1) operation to reach 1 in the Collatz conjecture.
%C Also, members of A023758 divisible by 3, divided by 3 (conjectured).
%H Andreas M. Hinz and Paul K. Stockmeyer, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL25/Hinz/hinz5.html">Precious Metal Sequences and Sierpinski-Type Graphs</a>, J. Integer Seq., Vol 25 (2022), Article 22.4.8.
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>.
%F a(n) = (4 * 2^A055086(n-1) - 2^A082375(n-1))/3. - _André Hallqvist_, Jul 17 2019
%F Sum_{n>=1} 1/a(n) = 2 * A321873 = 2.5265861162... . - _Amiram Eldar_, Jul 19 2022
%t Select[Range[2600], IntegerQ@ Log[4, 3 # + 1] &@ NestWhile[#/2 &, #, IntegerQ[#/2] &] &] (* _Michael De Vlieger_, May 12 2017 *)
%o (PARI) for(n=2, 2000, o=3*n/2^valuation(n,2)+1; b=ispower(o); if(b&&round(sqrtn(o,b\2))==4, print1(n, ", ")))
%o (Python)
%o for a in range(2, 17):
%o print()
%o for b in range(a - 2, -1, -2):
%o print(((1 << a) - (1 << b)) // 3, end=", ")
%o # _André Hallqvist_, Jul 25 2019
%o # This script shows the sequence as an irregular table whose main diagonal is A000975, called the "Lichtenberg sequence" by _Andreas M. Hinz_. - _Peter Luschny_, Jul 10 2022
%Y Cf. A023758, A055086, A082375, A000975, A321873.
%K nonn
%O 1,2
%A _Ralf Stephan_, Nov 18 2010
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