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).
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
Examples
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}
...
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.
Crossrefs
Programs
-
Mathematica
Join[{{2}}, Map[PositionIndex[Reverse[IntegerDigits[#, 2]]][1] &, Select[Range[4, 400, 4], DigitCount[#, 2, 1] < IntegerExponent[#, 2] + 1 &]]]
Formula
T(n,k) = A373359(n,k) + 1.
Comments