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A373579 Irregular triangle read by rows where row n lists (in increasing order) the elements of the strong Schreier set encoded by A371176(2*n).

%I A373579 #13 Jun 25 2024 17:07:43
%S A373579 2,3,4,3,4,5,3,5,4,5,6,3,6,4,6,5,6,4,5,6,7,3,7,4,7,5,7,4,5,7,6,7,4,6,
%T A373579 7,5,6,7,8,3,8,4,8,5,8,4,5,8,6,8,4,6,8,5,6,8,7,8,4,7,8,5,7,8,6,7,8,5,
%U A373579 6,7,8,9,3,9,4,9,5,9,4,5,9,6,9,4,6,9,5,6,9
%N A373579 Irregular triangle read by rows where row n lists (in increasing order) the elements of the strong Schreier set encoded by A371176(2*n).
%C A373579 See A373557 (where elements in each set are listed in decreasing order) for more information.
%H A373579 Paolo Xausa, <a href="/A373579/b373579.txt">Table of n, a(n) for n = 1..10000</a> (rows 1..2261 of the triangle, flattened).
%H A373579 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 A373579 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.
%F A373579 T(n,k) = A373359(n,k) + 1.
%e A373579 Triangle begins:
%e A373579                                         Corresponding
%e A373579    n  A371176(2*n)  bin(A371176(2*n))   strong Schreier set
%e A373579                                         (this sequence)
%e A373579   ---------------------------------------------------------
%e A373579    1        2               10          {2}
%e A373579    2        4              100          {3}
%e A373579    3        8             1000          {4}
%e A373579    4       12             1100          {3, 4}
%e A373579    5       16            10000          {5}
%e A373579    6       20            10100          {3, 5}
%e A373579    7       24            11000          {4, 5}
%e A373579    8       32           100000          {6}
%e A373579    9       36           100100          {3, 6}
%e A373579   10       40           101000          {4, 6}
%e A373579   11       48           110000          {5, 6}
%e A373579   12       56           111000          {4, 5, 6}
%e A373579   ...
%t A373579 Join[{{2}}, Map[PositionIndex[Reverse[IntegerDigits[#, 2]]][1] &, Select[Range[4, 400, 4], DigitCount[#, 2, 1] < IntegerExponent[#, 2] + 1 &]]]
%Y A373579 Subsequence of A373359.
%Y A373579 Cf. A007895 (conjectured row lengths), A371176, A373557, A373558, A373853 (row sums).
%K A373579 nonn,tabf,base,easy
%O A373579 1,1
%A A373579 _Paolo Xausa_, Jun 10 2024