%I A002251
%S A002251 0,2,1,5,7,3,10,4,13,15,6,18,20,8,23,9,26,28,11,31,12,34,36,14,39,
%T A002251 41,16,44,17,47,49,19,52,54,21,57,22,60,62,24,65,25,68,70,27,73,75,
%U A002251 29,78,30,81,83,32,86,33,89,91,35,94,96,37,99,38,102,104,40,107,109
%N A002251 Start with sequence of nonnegative integers; then swap L(k) and U(k) 
               for all k >= 1, where L = A000201, U = A001950 (lower and upper Wythoff 
               sequences).
%C A002251 (n,a(n)) are Wythoff pairs: (0,0),(1,2),(3,5),(4,7),..., where each difference 
               occurs once.
%C A002251 Self-inverse when considered as a permutation or function, i.e. a(a(n)) 
               = n. - Howard A. Landman (howard(AT)polyamory.org), Sep 25 2001
%C A002251 If the offset is 1, the sequence can also be obtained by rearranging 
               the natural numbers so that sum of n terms is a multiple of n, or 
               equivalently so that the arithmetic mean of the first n terms is 
               an integer. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Aug 
               16 2002
%C A002251 For n=1,2,3,..., let p(n)=least natural number not already an a(k), q(n)=n+p(n); 
               then a(p(n))=q(n), a(q(n))=p(n). - Clark Kimberling (ck6(AT)evansville.edu)
%C A002251 Also, indices of powers of 2 in A086482. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), 
               Jul 26 2003
%D A002251 E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, 
               NY, 2 vols., 1982, see p. 76.
%D A002251 R. Silber, Wythoff's Nim and Fibonacci Representations, Fibonacci Quarterly 
               #14 (1977), pp. 85-88.
%H A002251 <a href="Sindx_Per.html#IntegerPermutation">Index entries for sequences 
               that are permutations of the natural numbers</a>
%Y A002251 A002251 maps between A000201 and A001950, in that A002251(A000201(n)) 
               = A001950(n), A002251(A001950(n)) = A000201(n). A019444 = A002251 
               + 1.
%Y A002251 Row 0 of A018219. Cf. A073869.
%Y A002251 Sequence in context: A059039 A109261 A085240 this_sequence A093545 A005297 
               A014551
%Y A002251 Adjacent sequences: A002248 A002249 A002250 this_sequence A002252 A002253 
               A002254
%K A002251 nonn,easy,nice
%O A002251 0,2
%A A002251 Michael Kleber, michael.kleber(AT)gmail.com
%E A002251 Edited by Christian G. Bower (bowerc(AT)usa.net), Oct 29 2002