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

%I A373359 #23 Jun 22 2024 18:22:43
%S A373359 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,
%T A373359 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,
%U A373359 5,6,7,8,2,8,3,8,4,8,3,4,8,5,8,3,5,8,4,5,8,6,8
%N A373359 Irregular triangle read by rows where row n lists (in increasing order) the elements of the Schreier set encoded by A371176(n).
%C A373359 See A373345 (where elements in each set are listed in decreasing order) for more information.
%H A373359 Paolo Xausa, <a href="/A373359/b373359.txt">Table of n, a(n) for n = 1..10000</a> (rows 1..2261 of the triangle, flattened).
%H A373359 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.
%F A373359 T(n,k) = A373579(n,k) - 1.
%e A373359 Triangle begins:
%e A373359                                    Corresponding Schreier
%e A373359    n  A371176(n)  bin(A371176(n))  set (this sequence)
%e A373359   -------------------------------------------------------
%e A373359    1      1              1         {1}
%e A373359    2      2             10         {2}
%e A373359    3      4            100         {3}
%e A373359    4      6            110         {2, 3}
%e A373359    5      8           1000         {4}
%e A373359    6     10           1010         {2, 4}
%e A373359    7     12           1100         {3, 4}
%e A373359    8     16          10000         {5}
%e A373359    9     18          10010         {2, 5}
%e A373359   10     20          10100         {3, 5}
%e A373359   11     24          11000         {4, 5}
%e A373359   12     28          11100         {3, 4, 5}
%e A373359   ...
%t A373359 Join[{{1}}, Map[PositionIndex[Reverse[IntegerDigits[#, 2]]][1] &, Select[Range[2, 200, 2], DigitCount[#, 2, 1] <= IntegerExponent[#, 2] + 1 &]]]
%Y A373359 Cf. A371176, A373345, A373558, A373579.
%Y A373359 Cf. A007895 (conjectured row lengths), A373346 (row sums), A373347.
%K A373359 nonn,tabf,easy,base
%O A373359 1,2
%A A373359 _Paolo Xausa_, Jun 04 2024