A363011 Indices of record highs in A362816.
1, 3, 9, 57, 504, 3847, 41170
Offset: 1
Examples
Cf. A362815, A362816.
Links
- Samuel Harkness, MATLAB program
Programs
-
MATLAB
See Links section.
This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Cf. A362815, A362816.
See Links section.
For a(9), we first try 1. If a(9) were 1, {a(3), a(6), a(9)} would be {1, 1, 1}, but this already occurred at {a(1), a(2), a(3)}.
Next, try 2. If a(9) were 2, {a(3), a(6), a(9)} would be {1, 1, 2}, but this already occurred at {a(2), a(3), a(4)}.
Next, try 3. If a(9) were 3, {a(3), a(6), a(9)} would be {1, 1, 3}, but this already occurred at {a(1), a(3), a(5)}.
Next, try 4. If a(9) were 4, {a(1), a(5), a(9)} would be {1, 3, 4}, but this already occurred at {a(2), a(5), a(8)}.
Then, try 5. New subsequences at indices {a(1), a(5), a(9)} = {1, 3, 5}, {a(3), a(6), a(9)} = {1, 1, 5}, {a(5), a(7), a(9)} = {3, 2, 5}, and {a(7), a(8), a(9)} = {2, 4, 5} are formed, none of which have occurred at any {a(j), a(j+k), a(j+2k)} (for any j and k) previously. No 5 has occurred previously, so criteria (2) in Comments must be satisfied. Thus a(9) = 5.
a(10) is the first time a candidate is denied solely because it would create a guaranteed future duplicate. Note that no subsequences prevent a(10) from being 4.
n = 1 2 3 4 5 6 7 8 9 10 11 12 13 14
a(n) = 1 1 1 2 3 1 2 4 5 [4] X
| | |
| | |
If a(10) were 4, {a(2), a(8), a(14)} = {a(6), a(10), a(14)} = {1, 4, X}, making a subsequence {a(j), a(j+k), a(j+2k)} which is not unique. Therefore a(10) != 4.
See Links section. (C++) See Links section.
2 is in the sequence.
For 3: the only arithmetic progression made with 3 is p = {2,3}. Here, length(p) = min(p), so 3 is a term.
For 4: p = {2,3,4} can be made. Here, length(p) > min(p), so 4 is not a term.
For 5: the only arithmetic progressions made with 5 are p = {2,5} and p = {3,5}. Neither of these have length(p) > min(p), so 5 is a term.
...
For 9: p = {3,5,7,9} can be made. Here, length(p) > min(p), so 9 is not a term.
See Links section.
Comments