A248147 Table read by rows: n-th row contains all consecutive subsets of the first n primes in their natural order.

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, 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, 3, 5, 7, 11, 2, 3, 5, 7, 11, 13, 2, 3, 3, 5, 5, 7, 7, 11

Offset: 1

Author

Reinhard Zumkeller, Oct 02 2014

Keywords

• nonn
• tabf

Comments

A000292(n) = length of n-th row, whereas A000217(n) = number of all consecutive subsets of numbers 1..n;

T(n,k) = A000040(A248141(n,k)), 1 <= k <= A000292(n).

Examples

			.  1: 2
.  2: 2,3,2,3
.  3: 2,3,5,2,3,3,5,2,3,5
.  4: 2,3,5,7,2,3,3,5,5,7,2,3,5,3,5,7,2,3,5,7
.  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,...
rows concatenated from:
.  1: [2]
.  2: [2] [3] [2,3]
.  3: [2] [3] [5] [2,3] [3,5] [2,3,5]
.  4: [2] [3] [5] [7] [2,3] [3,5] [5,7] [2,3,5] [3,5,7] [2,3,5,7]
.  5: [2] [3] [5] [7] [11] [2,3] [3,5] [5,7] [7,11] [2,3,5] [3,5,7] ...
		

Links

• Reinhard Zumkeller, Rows n = 1..20 of triangle, flattened

Crossrefs

Cf. A151800, A000292, A000217, A248164, A248141.

Programs

Haskell

import Data.List (group)
a248147 n k = a248147_tabf !! (n-1) !! (k-1)
a248147_row n = a248147_tabf !! (n-1)
a248147_tabf = map concat psss where
   psss = iterate f [[2]] where
      f pss = group (h $ last pss) ++ map h pss
      h ws = ws ++ [a151800 $ last ws]