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%I #14 Sep 18 2021 09:03:37
%S 1,3,2,4,6,8,5,7,9,11,16,21,10,12,14,19,24,29,13,15,17,22,27,32,37,42,
%T 18,20,25,30,35,40,45,50,55,23,28,33,38,43,48,53,58,63,26,31,36,41,46,
%U 51,56,61,66,71,76,34,39,44,49,54,59,64,69,74,79,84,97,110,47,52,57,62
%N Preliminary Wythoff Triangle, P.
%C Every positive integer occurs exactly once, so that this is a permutation of the natural numbers.
%C Arranging each row in increasing order results in the Wythoff triangle (A166310).
%D Clark Kimberling, "The Wythoff triangle and unique representations of positive integers," Proceedings of the Fourteenth International Conference on Fibonacci Numbers and Their Applications," Aportaciones Matematicas Invertigacion 20 (2011) 155-169.
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F For a=1,2,3,... and b=0,1,...,a-1, let P(a,b) be the number of the row of the Wythoff array (A035513) that precurses to (a,b).
%e The first six rows of P:
%e 1
%e 3....2
%e 4....6...8
%e 5....7...9..11
%e 16..21..10..12..14
%e 19..24..29..13..15..17
%e The Wythoff array W begins with
%e 1...2...3...5...
%e 4...7..11..18...
%e 6..10..16..26...
%e These rows precurse to rows of the left-justified Wythoff array (A165357):
%e 1...0...1...1...1...2...3...
%e 2...1...3...4...7..11..18...
%e 2...0...2...2...4...6..10...
%e P(2,0)=3 because row 3 of W precurses to (2,0).
%e P(2,1)=2 because row 2 of W precurses to (2,1).
%Y Cf. A035513, A165357.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Oct 11 2009
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