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%I #5 Oct 05 2014 09:28:40
%S 2,2,3,2,3,2,3,5,2,3,3,5,2,3,5,2,3,5,7,2,3,3,5,5,7,2,3,5,3,5,7,2,3,5,
%T 7,2,3,5,7,11,2,3,3,5,5,7,7,11,2,3,5,3,5,7,5,7,11,2,3,5,7,3,5,7,11,2,
%U 3,5,7,11,2,3,5,7,11,13,2,3,3,5,5,7,7,11
%N Table read by rows: n-th row contains all consecutive subsets of the first n primes in their natural order.
%C A000292(n) = length of n-th row, whereas A000217(n) = number of all consecutive subsets of numbers 1..n;
%C T(n,k) = A000040(A248141(n,k)), 1 <= k <= A000292(n).
%H Reinhard Zumkeller, <a href="/A248147/b248147.txt">Rows n = 1..20 of triangle, flattened</a>
%e . 1: 2
%e . 2: 2,3,2,3
%e . 3: 2,3,5,2,3,3,5,2,3,5
%e . 4: 2,3,5,7,2,3,3,5,5,7,2,3,5,3,5,7,2,3,5,7
%e . 5: 2,3,5,7,11,2,3,3,5,5,7,7,11,2,3,5,3,5,7,5,7,11,2,3,5,7,3,5,7,11,...
%e rows concatenated from:
%e . 1: [2]
%e . 2: [2] [3] [2,3]
%e . 3: [2] [3] [5] [2,3] [3,5] [2,3,5]
%e . 4: [2] [3] [5] [7] [2,3] [3,5] [5,7] [2,3,5] [3,5,7] [2,3,5,7]
%e . 5: [2] [3] [5] [7] [11] [2,3] [3,5] [5,7] [7,11] [2,3,5] [3,5,7] ...
%o (Haskell)
%o import Data.List (group)
%o a248147 n k = a248147_tabf !! (n-1) !! (k-1)
%o a248147_row n = a248147_tabf !! (n-1)
%o a248147_tabf = map concat psss where
%o psss = iterate f [[2]] where
%o f pss = group (h $ last pss) ++ map h pss
%o h ws = ws ++ [a151800 $ last ws]
%Y Cf. A151800, A000292, A000217, A248164, A248141.
%K nonn,tabf
%O 1,1
%A _Reinhard Zumkeller_, Oct 02 2014
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