A373558 Irregular triangle read by rows: T(1,1) = 1 and, for n >= 2, row n lists (in increasing order) the elements of the maximal Schreier set encoded by 2*A355489(n-1).

1, 2, 3, 2, 4, 2, 5, 3, 4, 5, 2, 6, 3, 4, 6, 3, 5, 6, 2, 7, 3, 4, 7, 3, 5, 7, 3, 6, 7, 4, 5, 6, 7, 2, 8, 3, 4, 8, 3, 5, 8, 3, 6, 8, 4, 5, 6, 8, 3, 7, 8, 4, 5, 7, 8, 4, 6, 7, 8, 2, 9, 3, 4, 9, 3, 5, 9, 3, 6, 9, 4, 5, 6, 9, 3, 7, 9, 4, 5, 7, 9, 4, 6, 7, 9, 3, 8, 9

Offset

1,2

Comments

See A373556 (where elements in each set are listed in decreasing order) for more information.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10003 (rows 1..1892 of the triangle, flattend).

Alistair Bird, Jozef Schreier, Schreier sets and the Fibonacci sequence, Out Of The Norm blog, May 13 2012.

Hùng Việt Chu, The Fibonacci Sequence and Schreier-Zeckendorf Sets, Journal of Integer Sequences, Vol. 22 (2019), Article 19.6.5.

Example

Triangle begins:
                                           Corresponding
   n  2*A355489(n-1)  bin(2*A355489(n-1))  maximal Schreier set
                                           (this sequence)
  ---------------------------------------------------------------
   1                                       {1}
   2         6                 110         {2, 3}
   3        10                1010         {2, 4}
   4        18               10010         {2, 5}
   5        28               11100         {3, 4, 4}
   6        34              100010         {2, 6}
   7        44              101100         {3, 4, 6}
   8        52              110100         {3, 5, 6}
   9        66             1000010         {2, 7}
  10        76             1001100         {3, 4, 7}
  11        84             1010100         {3, 5, 7}
  12       100             1100100         {3, 6, 7}
  13       120             1111000         {4, 5, 6, 7}
  ...

Mathematica

Join[{{1}}, Map[PositionIndex[Reverse[IntegerDigits[#, 2]]][1] &, Select[Range[2, 500, 2], DigitCount[#, 2, 1] == IntegerExponent[#, 2] + 1 &]]]

Crossrefs

Subsequence of A373359.

Cf. A143299 (conjectured row lengths), A355489, A373556, A373579, A373854 (row sums).

Sequence in context: A365791 A331252 A162908 * A222817 A344324 A309428

Adjacent sequences: A373555 A373556 A373557 * A373559 A373560 A373561

Keyword

nonn,tabf,base,easy

Author

Paolo Xausa, Jun 10 2024

Status

approved