A373359 Irregular triangle read by rows where row n lists (in increasing order) the elements of the Schreier set encoded by A371176(n).

1, 2, 3, 2, 3, 4, 2, 4, 3, 4, 5, 2, 5, 3, 5, 4, 5, 3, 4, 5, 6, 2, 6, 3, 6, 4, 6, 3, 4, 6, 5, 6, 3, 5, 6, 4, 5, 6, 7, 2, 7, 3, 7, 4, 7, 3, 4, 7, 5, 7, 3, 5, 7, 4, 5, 7, 6, 7, 3, 6, 7, 4, 6, 7, 5, 6, 7, 4, 5, 6, 7, 8, 2, 8, 3, 8, 4, 8, 3, 4, 8, 5, 8, 3, 5, 8, 4, 5, 8, 6, 8

Offset: 1

Author

Paolo Xausa, Jun 04 2024

Keywords

• nonn
• tabf
• easy
• base

Comments

See A373345 (where elements in each set are listed in decreasing order) for more information.

Examples

			Triangle begins:
                                   Corresponding Schreier
   n  A371176(n)  bin(A371176(n))  set (this sequence)
  -------------------------------------------------------
   1      1              1         {1}
   2      2             10         {2}
   3      4            100         {3}
   4      6            110         {2, 3}
   5      8           1000         {4}
   6     10           1010         {2, 4}
   7     12           1100         {3, 4}
   8     16          10000         {5}
   9     18          10010         {2, 5}
  10     20          10100         {3, 5}
  11     24          11000         {4, 5}
  12     28          11100         {3, 4, 5}
  ...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000 (rows 1..2261 of the triangle, flattened).
• Alistair Bird, Jozef Schreier, Schreier sets and the Fibonacci sequence, Out Of The Norm blog, May 13 2012.

Crossrefs

Cf. A371176, A373345, A373558, A373579.

Cf. A007895 (conjectured row lengths), A373346 (row sums), A373347.

Programs

Mathematica

Join[{{1}}, Map[PositionIndex[Reverse[IntegerDigits[#, 2]]][1] &, Select[Range[2, 200, 2], DigitCount[#, 2, 1] <= IntegerExponent[#, 2] + 1 &]]]

Formula

T(n,k) = A373579(n,k) - 1.