OFFSET
1,2
COMMENTS
A maximal Schreier set is a subset of the positive integers with cardinality equal to the minimum element in the set (see Chu link).
For n >= 2, each term k = 2*A355489(n-1) can be put into a one-to-one correspondence with a maximal Schreier set by interpreting the 1-based position of the ones in the binary expansion of k (where position 1 corresponds to the least significant bit) as the elements of the corresponding maximal Schreier set.
See A373558 for the elements in each set arranged in increasing order.
The number of sets having maximum element m (for m >= 2) is A000045(m-2).
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
(this sequence)
---------------------------------------------------------------
1 {1}
2 6 110 {3, 2}
3 10 1010 {4, 2}
4 18 10010 {5, 2}
5 28 11100 {5, 4, 3}
6 34 100010 {6, 2}
7 44 101100 {6, 4, 3}
8 52 110100 {6, 5, 3}
9 66 1000010 {7, 2}
10 76 1001100 {7, 4, 3}
11 84 1010100 {7, 5, 3}
12 100 1100100 {7, 6, 3}
13 120 1111000 {7, 6, 5, 4}
...
MATHEMATICA
Join[{{1}}, Map[Reverse[PositionIndex[Reverse[IntegerDigits[#, 2]]][1]] &, Select[Range[2, 500, 2], DigitCount[#, 2, 1] == IntegerExponent[#, 2] + 1 &]]]
CROSSREFS
KEYWORD
nonn,tabf,base,easy
AUTHOR
Paolo Xausa, Jun 09 2024
STATUS
approved