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A064790 Inverse permutation to A060734.

%I A064790 #26 Feb 16 2025 08:32:45
%S A064790 1,3,5,2,6,9,13,8,4,10,14,19,25,18,12,7,15,20,26,33,41,32,24,17,11,21,
%T A064790 27,34,42,51,61,50,40,31,23,16,28,35,43,52,62,73,85,72,60,49,39,30,22,
%U A064790 36,44,53,63,74,86,99,113,98,84,71,59,48,38,29,45,54,64,75,87,100,114
%N A064790 Inverse permutation to A060734.
%C A064790 From _Boris Putievskiy_, Mar 14 2013: (Start)
%C A064790 a(n) is a pairing function: a function that reversibly maps Z^{+} x Z^{+} onto Z^{+}, where Z^{+} is the set of integer positive numbers.
%C A064790 Layer is pair of sides of square from T(1,n) to T(n,n) and  from T(n,n) to T(n,1). This sequence is A188568 as table read  by boustrophedonic ("ox-plowing") method - layer clockwise, layer counterclockwise and so. The same table A188568 read layer by layer clockwise is A194280. (End)
%H A064790 Boris Putievskiy, <a href="http://arxiv.org/abs/1212.2732">Transformations Integer Sequences And Pairing Functions</a>, arXiv:1212.2732 [math.CO], 2012.
%H A064790 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>
%H A064790 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A064790 a(n) = (i+j-1)*(i+j-2)/2+i, where i=min(t; t^2-n+1), j=min(t; n-(t-1)^2), t=floor(sqrt(n-1))+1. - _Boris Putievskiy_, Dec 24 2012
%e A064790 From _Boris Putievskiy_, Mar 14 2013: (Start)
%e A064790 The start of the sequence as table:
%e A064790   1....2...6...7..15..16..28...
%e A064790   3....5...9..12..20..23..35...
%e A064790   4....8..13..18..26..31..43...
%e A064790   10..14..19..25..33..40..52...
%e A064790   11..17..24..32..41..50..62...
%e A064790   21..27..34..42..51..61..73...
%e A064790   22..30..39..49..60..72..85...
%e A064790   ...
%e A064790 The start of the sequence as triangular array read by rows:
%e A064790   1;
%e A064790   3,5,2;
%e A064790   6,9,13,8,4;
%e A064790   10,14,19,25,18,12,7;
%e A064790   15,20,26,33,41,32,24,17,11;
%e A064790   21,27,34,42,51,61,50,40,31,23,16;
%e A064790   28,35,43,52,62,73,85,72,60,49,39,30,22;
%e A064790   ...
%e A064790 Row number r contains 2*r-1 numbers. (End)
%Y A064790 Cf. A060734, A064788, A188568, A194280.
%K A064790 nonn,easy
%O A064790 1,2
%A A064790 _N. J. A. Sloane_, Oct 20 2001