%I #19 Sep 30 2017 02:33:06
%S 1,3,4,2,7,8,6,9,5,13,14,12,15,11,16,10,21,22,20,23,19,24,18,25,17,31,
%T 32,30,33,29,34,28,35,27,36,26,43,44,42,45,41,46,40,47,39,48,38,49,37,
%U 57,58,56,59,55,60,54,61,53,62,52,63,51,64,50,73,74,72,75,71,76,70,77
%N Group the natural numbers into blocks: B_1 = 1, B_2 = 2,3,4, B_3 = 5,6,7,8,9, ..., each block ending in a square. Permute each block B_k by beginning with the central term, followed by the transposed symmetric pairs from B_k.
%C A permutation of the natural numbers.
%H S. G. Krantz and J. D. McNeal, <a href="http://www.jstor.org/stable/4145013">Creating more convergent series</a>, Amer. Math. Monthly, 111 (No. 1, 2004), 32-38.
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F The k-th term of the n-th block is T(n, k) = n^2-n+1+(-1)^k*floor(k/2), k=1..2*n-1. - _Vladeta Jovovic_, Jan 16 2004
%e B_4 = 10,11,12,13,14,15,16 becomes 13, 14,12, 15,11, 16,10.
%e 1; 3,4,2; 7,8,6,9,5; 13,14,12,15,11,16,10; ...
%t pb[c_]:=Module[{len=(Length[c]-1)/2},Flatten[Join[{c[[len+1]]}, Thread[ {Take[c,-len],Reverse[Take[c,len]]}]]]] ; Flatten[pb/@ Table[Range[ (n-1)^2+1,n^2],{n,10}]] (* _Harvey P. Dale_, Jun 18 2015 *)
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Jan 16 2004
%E More terms from _Vladeta Jovovic_, Jan 16 2004