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A099730 Array read by antidiagonals. Rows contain odd numbers reaching same odd successor in Collatz function iteration.

%I A099730 #27 Aug 28 2015 17:51:46
%S A099730 1,5,3,21,13,7,85,53,29,9,341,213,117,37,11,1365,853,469,149,45,15,
%T A099730 5461,3413,1877,597,181,61,17,21845,13653,7509,2389,725,245,69,19,
%U A099730 87381,54613,30037,9557,2901,981,277,77,23
%N A099730 Array read by antidiagonals. Rows contain odd numbers reaching same odd successor in Collatz function iteration.
%C A099730 All numbers that end in 3 will begin with numbers from previous row (for example, 3413 is 341&3). - _Jean-Bernard François_, Sep 09 2013
%C A099730 The sequence is a permutation of the odd positive integers. - _Bob Selcoe_, Jul 26 2015
%F A099730 Let g(n)= floor((n+1)/3), then T(n,k) = 2^(2*(k+1)-1) *(n+g(n)) + (4^(k+1)-1)/3. - _Maon Wenders_, Jul 15 2012
%F A099730 t(n, k) = 4*t(n, k-1) + 1. - _Jean-Bernard François_, Sep 09 2013
%e A099730 t(1, 2) = 53 = 4*13+1, t(2, 5) = 7509 = 4*1877+1.
%e A099730 Array begins:
%e A099730 1 5 21 85 341 1365 5461 21845 87381 ...
%e A099730 3 13 53 213 853 3413 13653 54613 218453 ...
%e A099730 7 29 117 469 1877 7509 30037 120149 480597 ...
%e A099730 9 37 149 597 2389 9557 38229 152917 611669 ...
%e A099730 11 45 181 725 2901 11605 46421 185685 742741 ...
%e A099730 15 61 245 981 3925 15701 62805 251221 1004885 ...
%e A099730 17 69 277 1109 4437 17749 70997 283989 1135957 ...
%e A099730 19 77 309 1237 4949 19797 79189 316757 1267029 ...
%e A099730 ...
%e A099730 Construct array by writing odd numbers in columns, taking first overflow after two steps and then an overflow each fourth step (for each column).
%t A099730 t[n_, k_] := 2^(2*(k + 1) - 1)*(n + Quotient[n + 1, 3]) + (4^(k + 1) - 1)/3; Table[t[n - k, k], {n, 0, 8}, {k, n, 0, -1}] // Flatten (* _Jean-François Alcover_, Sep 09 2013, after _Maon Wenders_ *)
%o A099730 (PARI) g(n)=(n+1)\3
%o A099730 T(n,k)=2^(2*(k+1)-1)*(n+g(n))+(4^(k+1)-1)/3
%o A099730 for(i=0,20,for(j=0,10,print1(T(i,j), ", "));print())\\ _Maon Wenders_, Jul 15 2012
%Y A099730 First row = A002450 (except leading zero), second row = A072197, third row = A072261.
%K A099730 nonn,tabl
%O A099730 1,2
%A A099730 Lambert Klasen (lambert.klasen(AT)gmx.de), Nov 09 2004