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%I #24 Sep 25 2015 15:45:26
%S 1,1,1,1,1,2,1,1,1,2,1,3,2,4,1,1,1,2,1,3,2,4,1,5,3,6,2,7,4,8,1,1,1,2,
%T 1,3,2,4,1,5,3,6,2,7,4,8,1,9,5,10,3,11,6,12,2,13,7,14,4,15,8,16,1,1,1,
%U 2,1,3,2,4,1,5,3,6,2,7,4,8,1,9,5,10,3,11,6,12,2,13,7,14,4,15,8,16
%N Triangle read by rows in which row n lists the first 2^(n-1) terms of A003602.
%C The old definition (see history #7) was:
%C "Numbers such that n is contained in the array a(n) where array 1 is A099627, array 2 is A124922 etc. (Table A167979 illustrates the manner in which the array numbers are chosen - e.g. "12" is not in array 1 or 2 so it begins array 3. All of the arrays can be seen in A161924."
%e From _Omar E. Pol_, Feb 21 2011: (Start)
%e If written as a triangle:
%e 1,
%e 1,1,
%e 1,1,2,1,
%e 1,1,2,1,3,2,4,1,
%e 1,1,2,1,3,2,4,1,5,3,6,2,7,4,8,1,
%e 1,1,2,1,3,2,4,1,5,3,6,2,7,4,8,1,9,5,10,3,11,6,12,2,13,7,14,4,15,8,16,1,
%e ...
%e (End)
%e a(12)= 3 therefore, as expected, 12 is contained in array 3; a(14)= 4 so 14 is a member of array 4, etc.
%e A099627 (array 1) begins 1 2 3 4 5 7 8 9 11 15 ...
%e A124922 (array 2) begins 6 10 13 18 21 27 ... so a(n) begins 1 1 1 1 1 2 1 1 1 2 1 ...
%e The next two arrays begin 12 20 25 36 41 51 ... and 14 22 29 38 45 59 ...
%Y Cf. A003602, A099627, A124922, A167201 (uses array 3), A167202 (uses array 4), A161924 (contains all of the arrays), A167979 (Linearizes and concatenates the arrays).
%K easy,nonn,tabf
%O 1,6
%A _Alford Arnold_, Nov 12 2009
%E Definition corrected by _Alford Arnold_, Feb 05 2011
%E Better definition from _Omar E. Pol_, Feb 21 2011
%E Further edits from _N. J. A. Sloane_, Feb 21 2011
%E More terms a(64)-a(94) from _Omar E. Pol_, Feb 22 2011
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