A373558 - OEIS

%I #19 Jun 25 2024 17:07:35

%S 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,

%T 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,

%U 6,9,4,5,6,9,3,7,9,4,5,7,9,4,6,7,9,3,8,9

%N 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).

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

%H Paolo Xausa, <a href="/A373558/b373558.txt">Table of n, a(n) for n = 1..10003</a> (rows 1..1892 of the triangle, flattend).

%H Alistair Bird, <a href="https://outofthenormmaths.wordpress.com/2012/05/13/jozef-schreier-schreier-sets-and-the-fibonacci-sequence/">Jozef Schreier, Schreier sets and the Fibonacci sequence</a>, Out Of The Norm blog, May 13 2012.

%H Hùng Việt Chu, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL22/Chu2/chu9.pdf">The Fibonacci Sequence and Schreier-Zeckendorf Sets</a>, Journal of Integer Sequences, Vol. 22 (2019), Article 19.6.5.

%e Triangle begins:

%e                                            Corresponding

%e    n  2*A355489(n-1)  bin(2*A355489(n-1))  maximal Schreier set

%e                                            (this sequence)

%e   ---------------------------------------------------------------

%e    1                                       {1}

%e    2         6                 110         {2, 3}

%e    3        10                1010         {2, 4}

%e    4        18               10010         {2, 5}

%e    5        28               11100         {3, 4, 4}

%e    6        34              100010         {2, 6}

%e    7        44              101100         {3, 4, 6}

%e    8        52              110100         {3, 5, 6}

%e    9        66             1000010         {2, 7}

%e   10        76             1001100         {3, 4, 7}

%e   11        84             1010100         {3, 5, 7}

%e   12       100             1100100         {3, 6, 7}

%e   13       120             1111000         {4, 5, 6, 7}

%e   ...

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

%Y Subsequence of A373359.

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

%K nonn,tabf,base,easy

%O 1,2

%A _Paolo Xausa_, Jun 10 2024