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.
%I A062880 #64 Aug 22 2023 08:01:58
%S A062880 0,2,8,10,32,34,40,42,128,130,136,138,160,162,168,170,512,514,520,522,
%T A062880 544,546,552,554,640,642,648,650,672,674,680,682,2048,2050,2056,2058,
%U A062880 2080,2082,2088,2090,2176,2178,2184,2186,2208,2210,2216,2218,2560,2562
%N A062880 Zero together with the numbers which can be written as a sum of distinct odd powers of 2.
%C A062880 Binary expansion of n does not contain 1-bits at even positions.
%C A062880 Integers whose base-4 representation consists of only 0's and 2's.
%C A062880 Every nonnegative even number is a unique sum of the form a(k)+2*a(l); moreover, this sequence is unique with such property. - _Vladimir Shevelev_, Nov 07 2008
%C A062880 Also numbers such that the digital sum base 2 and the digital sum base 4 are in a ratio of 2:4. - _Michel Marcus_, Sep 23 2013
%C A062880 From _Gus Wiseman_, Jun 10 2020: (Start)
%C A062880 Numbers k such that the k-th composition in standard order has all even parts. The k-th composition in standard order (graded reverse-lexicographic, A066099) is obtained by taking the set of positions of 1's in the reversed binary expansion of k, prepending 0, taking first differences, and reversing again. For example, the sequence of all compositions into even parts begins:
%C A062880 0: () 520: (6,4) 2080: (6,6)
%C A062880 2: (2) 522: (6,2,2) 2082: (6,4,2)
%C A062880 8: (4) 544: (4,6) 2088: (6,2,4)
%C A062880 10: (2,2) 546: (4,4,2) 2090: (6,2,2,2)
%C A062880 32: (6) 552: (4,2,4) 2176: (4,8)
%C A062880 34: (4,2) 554: (4,2,2,2) 2178: (4,6,2)
%C A062880 40: (2,4) 640: (2,8) 2184: (4,4,4)
%C A062880 42: (2,2,2) 642: (2,6,2) 2186: (4,4,2,2)
%C A062880 128: (8) 648: (2,4,4) 2208: (4,2,6)
%C A062880 130: (6,2) 650: (2,4,2,2) 2210: (4,2,4,2)
%C A062880 136: (4,4) 672: (2,2,6) 2216: (4,2,2,4)
%C A062880 138: (4,2,2) 674: (2,2,4,2) 2218: (4,2,2,2,2)
%C A062880 160: (2,6) 680: (2,2,2,4) 2560: (2,10)
%C A062880 162: (2,4,2) 682: (2,2,2,2,2) 2562: (2,8,2)
%C A062880 168: (2,2,4) 2048: (12) 2568: (2,6,4)
%C A062880 170: (2,2,2,2) 2050: (10,2) 2570: (2,6,2,2)
%C A062880 512: (10) 2056: (8,4) 2592: (2,4,6)
%C A062880 514: (8,2) 2058: (8,2,2) 2594: (2,4,4,2)
%C A062880 (End)
%H A062880 Reinhard Zumkeller, <a href="/A062880/b062880.txt">Table of n, a(n) for n = 0..10000</a>
%H A062880 D. H. Bailey, J. M. Borwein, R. E. Crandall, and C. Pomerance, <a href="http://dx.doi.org/10.5802/jtnb.457">On the binary expansions of algebraic numbers</a>, J. Théor. Nombres Bordeaux, 16 (2004), 487-518.
%H A062880 S. Eigen, A. Hajian, and S. Kalikow, <a href="http://dx.doi.org/10.1007/BF02787185">Ergodic transformations and sequences of integers</a>, Israel J. Math. 75 (1991), 119-128; Math. Rev. 1147294 (93c:28014).
%F A062880 a(n) = 2 * A000695(n). - _Vladimir Shevelev_, Nov 07 2008
%F A062880 From _Robert Israel_, Apr 10 2018: (Start)
%F A062880 a(2*n) = 4*a(n).
%F A062880 a(2*n+1) = 4*a(n)+2.
%F A062880 G.f. g(x) satisfies: g(x) = 4*(1+x)*g(x^2)+2*x/(1-x^2). (End)
%p A062880 [seq(a(j),j=0..100)]; a := n -> add((floor(n/(2^i)) mod 2)*(2^((2*i)+1)),i=0..floor_log_2(n+1));
%t A062880 b[n_] := BitAnd[n, Sum[2^k, {k, 0, Log[2, n] // Floor, 2}]]; Select[Range[ 0, 10^4], b[#] == 0&] (* _Jean-François Alcover_, Feb 28 2016 *)
%o A062880 (Haskell)
%o A062880 a062880 n = a062880_list !! n
%o A062880 a062880_list = filter f [0..] where
%o A062880 f 0 = True
%o A062880 f x = (m == 0 || m == 2) && f x' where (x', m) = divMod x 4
%o A062880 -- _Reinhard Zumkeller_, Nov 20 2012
%o A062880 (C) uint32_t a_next(uint32_t a_n) { return (a_n + 0x55555556) & 0xaaaaaaaa; } /* _Falk Hüffner_, Jan 22 2022 */
%o A062880 (Python)
%o A062880 def A062880(n): return int(bin(n)[2:],4)<<1 # _Chai Wah Wu_, Aug 21 2023
%Y A062880 Cf. A000695.
%Y A062880 Except for first term, n such that A063694(n) = 0. Binary expansion is given in A062033.
%Y A062880 Interpreted as Zeckendorf expansion: A062879.
%Y A062880 Central diagonal of arrays A163357 and A163359.
%Y A062880 Even partitions are counted by A035363.
%Y A062880 Numbers with an even number of 1's in binary expansion are A001969.
%Y A062880 Numbers whose binary expansion has even length are A053754.
%Y A062880 All of the following pertain to compositions in standard order (A066099):
%Y A062880 - Length is A000120.
%Y A062880 - Compositions without even parts are A060142.
%Y A062880 - Sum is A070939.
%Y A062880 - Product is A124758.
%Y A062880 - Strict compositions are A233564.
%Y A062880 - Heinz number is A333219.
%Y A062880 - Number of distinct parts is A334028.
%K A062880 nonn,easy
%O A062880 0,2
%A A062880 _Antti Karttunen_, Jun 26 2001