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%I #27 Oct 04 2020 14:39:23
%S 1,7,13,21,25,31,37,41,49,55,61,69,73,81,87,93,97,103,109,117,121,127,
%T 133,137,145,151,157,161,167,173,181,185,193,199,205,213,217,223,229,
%U 233,241,247,253,261,265,273,279,285,289,295
%N Odious twin locations: first members of pairs of consecutive odious numbers.
%C An odious number (A000069) is a nonnegative integer with an odd number of ones in its binary expansion.
%C In the reference it is shown that these odious twins alternate with the evil twins (see A157970), which are pairs of consecutive evil numbers (A001969) having even numbers of ones in their binary expansions.
%H Amiram Eldar, <a href="/A157971/b157971.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harvey P. Dale)
%H Chris Bernhardt, <a href="https://pdfslide.net/documents/evil-twins-alternate-with-odious-twins-fairfield-twinspdf-evil-twins-alternate.html">Evil twins alternate with odious twins</a>, Math. Mag. 82 (2009), pp. 57-62; also on <a href="https://www.jstor.org/stable/27643161">JSTOR</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/OdiousNumber.html">Odious Number</a>
%e The sequence of odious numbers (A000069) begins 1,2,4,7,8,11,13,14,16,19,21,..., so the first few odious twins are at 1,7,13, ... .
%t SequencePosition[Table[If[OddQ[DigitCount[n,2,1]],1,0],{n,300}],{1,1}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Oct 05 2016 *)
%o (PARI) lista(nn) = select(n->((hammingweight(n) % 2) && (hammingweight(n+1) % 2)), vector(nn, i, i)); \\ _Michel Marcus_, Jul 10 2014
%Y Cf. A000069, A091855, A157970.
%K nonn
%O 1,2
%A _John W. Layman_, Mar 10 2009
%E Comment corrected by _Jeff Aronson_. - _N. J. A. Sloane_, Oct 04 2020
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