A334950 Pairs (a,b) where "a" is the smallest candidate for the n-th term of Recamán's sequence and "b" is the n-th term of Recamán's sequence (A005132).
0, 0, -1, 1, -1, 3, 0, 6, 2, 2, -3, 7, 1, 13, 6, 20, 12, 12, 3, 21, 11, 11, 0, 22, 10, 10, -3, 23, 9, 9, -6, 24, 8, 8, -9, 25, 7, 43, 24, 62, 42, 42, 21, 63, 41, 41, 18, 18, -6, 42, 17, 17, -9, 43, 16, 16, -12, 44, 15, 15, -15, 45, 14, 14, -18, 46, 13, 79, 45, 113, 78, 78, 42, 114, 77, 77, 39, 39, 0, 78
Offset: 0
Keywords
Examples
Illustration of initial terms:
23
22 _
21 _ |
20 _ | | |
_ | | | | |
| | | | | | |
| | | | | | |
| | | | | | |
| | | | | | |
| | | | | | |
13 | | | | | | |
_ | | 12 | | | | |
| | | |_ _ | | 11 | | |
| | | | | |_ _ | | 10 |
| | | 12 | | | | |_ _ |
| | | | | 11 | | | |
7 | | | | | | | 10 | |
6 _ | | | | | | | | |
_ | | | |_| | | | | | |
| | | | | | | | | | |
3 | | | | | 6 | | | | | |
_ | | 2 | | | |_| | | | |
1 | | | |_ _ | | | | | | |
0 _ | | | | | |_| 3 | | | |
_ _ | | | |_| 2 | | |_| | |
|_| |_| | | 1 | |
0 0 | | 0 | |
-1 -1 |_| |_|
.
-3 -3
.
In the above diagram the numbers that are written below the path are the terms of A334951 (the candidates for A005132). The numbers that are written above the path are the terms of Recamán's sequence A005132. The length of the n-th vertical-line-segment equals the absolute value of A334952(n).
For n = 4, after A005132(4-1) = 6 the algorithm of Recamán's sequence first explores if A334951(4) = 6 - 4 = 2 is a valid number to be its 4th term. We can see that 2 is nonnegative and not already in Recamán's sequence, then it is accepted, so A005132(4) = A334951(4) = 2.
For n = 5, after A005132(5-1) = 2 the algorithm first explores if A334951(5) = 2 - 5 = -3 is a valid number to be its 5th term. We can see that -3 is negative, so -3 is rejected.
For n = 6, after A005132(6-1) = 7 the algorithm first explores if A334951(6) = 7 - 6 = 1 is a valid number to be its 6th term. We can see that 1 is already in Recamán's sequence, so 1 is rejected.
Comments