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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).
4
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, 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, 6, 7, 8, 9, 3, 9, 4, 9, 5, 9, 4, 5, 9, 6, 9, 4, 6, 9, 5, 6, 9
OFFSET
1,1
COMMENTS
See A373557 (where elements in each set are listed in decreasing order) for more information.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..10000 (rows 1..2261 of the triangle, flattened).
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.
FORMULA
T(n,k) = A373359(n,k) + 1.
EXAMPLE
Triangle begins:
Corresponding
n A371176(2*n) bin(A371176(2*n)) strong Schreier set
(this sequence)
---------------------------------------------------------
1 2 10 {2}
2 4 100 {3}
3 8 1000 {4}
4 12 1100 {3, 4}
5 16 10000 {5}
6 20 10100 {3, 5}
7 24 11000 {4, 5}
8 32 100000 {6}
9 36 100100 {3, 6}
10 40 101000 {4, 6}
11 48 110000 {5, 6}
12 56 111000 {4, 5, 6}
...
MATHEMATICA
Join[{{2}}, Map[PositionIndex[Reverse[IntegerDigits[#, 2]]][1] &, Select[Range[4, 400, 4], DigitCount[#, 2, 1] < IntegerExponent[#, 2] + 1 &]]]
CROSSREFS
Subsequence of A373359.
Cf. A007895 (conjectured row lengths), A371176, A373557, A373558, A373853 (row sums).
Sequence in context: A081399 A221108 A205554 * A336750 A336755 A214613
KEYWORD
nonn,tabf,base,easy
AUTHOR
Paolo Xausa, Jun 10 2024
STATUS
approved