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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).
4
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
KEYWORD
nonn,tabf,base,easy
AUTHOR
Paolo Xausa, Jun 10 2024
STATUS
approved