OFFSET
1,2
COMMENTS
Starting with a(1) = 1, this is the lexicographically earliest sequence with this property.
This is how the sequence was built:
1) start with the Natural numbers and increase the gaps between them by one unit (first gap is zero):
S = 1,2,_,3,_,_,4,_,_,_,5,_,_,_,_,6,_,_,_,_,_,7,_,_,_,_,_,_,8,_, ...
2) fill the empty spaces with the successive _starting_ chunks of the sequence S _itself_:
S = 1,2,_,3,_,_,4,_,_,_,5,_,_,_,_,6,_,_,_,_,_,7,_,_,_,_,_,_,8,_, ...
S = 1,2,1,3,_,_,4,_,_,_,5,_,_,_,_,6,_,_,_,_,_,7,_,_,_,_,_,_,8,_, ...
S = 1,2,1,3,1,2,4,_,_,_,5,_,_,_,_,6,_,_,_,_,_,7,_,_,_,_,_,_,8,_, ...
S = 1,2,1,3,1,2,4,1,2,1,5,_,_,_,_,6,_,_,_,_,_,7,_,_,_,_,_,_,8,_, ...
S = 1,2,1,3,1,2,4,1,2,1,5,1,2,1,3,6,_,_,_,_,_,7,_,_,_,_,_,_,8,_, ...
S = 1,2,1,3,1,2,4,1,2,1,5,1,2,1,3,6,1,2,1,3,1,7,_,_,_,_,_,_,8,_, ...
S = 1,2,1,3,1,2,4,1,2,1,5,1,2,1,3,6,1,2,1,3,1,7,1,2,1,3,1,2,8,_, ... Etc.
LINKS
Neal Gersh Tolunsky, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = a((n+1)*(n+2)/2).
EXAMPLE
One term out of 1 following a(1) = 1 is larger than 1: this is 2.
One term out of 2 following a(2) = 2 is larger than 2: this is 3.
One term out of 1 following a(3) = 1 is larger than 1: this is 2.
One term out of 3 following a(4) = 3 is larger than 3: this is 4.
One term out of 1 following a(5) = 1 is larger than 1: this is 2.
One term out of 2 following a(6) = 2 is larger than 2: this is 4.
One term out of 4 following a(7) = 4 is larger than 4: this is 5.
One term out of 1 following a(8) = 1 is larger than 1: this is 2.
One term out of 2 following a(9) = 2 is larger than 2: this is 5. Etc.
As triangle:
1;
2, 1;
3, 1, 2;
4, 1, 2, 1;
5, 1, 2, 1, 3;
6, 1, 2, 1, 3, 1;
7, 1, 2, 1, 3, 1, 2;
8, 1, 2, 1, 3, 1, 2, 4;
9, 1, 2, 1, 3, 1, 2, 4, 1;
10, 1, 2, 1, 3, 1, 2, 4, 1, 2;
...
MATHEMATICA
k=1; Nest[(k++; Join[#, #[[;; k-2]], {k}])&, {1}, 13] (* Giorgos Kalogeropoulos, Oct 03 2023 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Eric Angelini, Sep 29 2023
EXTENSIONS
Data corrected by Giorgos Kalogeropoulos, Oct 03 2023
STATUS
approved
