A180427 Lexicographically earliest permutation of the positive integers such that the inverse permutation is also the absolute value of the first differences.
1, 2, 4, 10, 13, 3, 19, 38, 16, 5, 9, 73, 48, 43, 23, 6, 15, 42, 7, 14, 45, 8, 49, 64, 12, 72, 17, 50, 97, 154, 20, 95, 27, 98, 18, 83, 21, 99, 91, 173, 22, 107, 89, 103, 190, 169, 28, 117, 104, 127, 155, 24, 118, 219, 26, 135, 29, 142, 258, 25, 147, 36, 181, 11, 35, 159
Offset: 1
Examples
Let a(n) be this sequence and b(n)=|a(n)-a(n+1)| be the inverse permutation of this sequence. After a(1)=1, a(2)=2, a(3)=4, the next term, a(4), cannot be a repeat of 1,2, or 4 since by definition a(n) must be a permutation of the positive integers. It cannot be 3,5, or 6, as that would force b(3)=1 or 2 (a repeat of b(1)=1, or b(2)=2). We cannot have a(4)=7, because b(3)=3 implies a(3)=3, which contradicts a(3)=4. We cannot have a(4)=8, because b(3)=4 implies a(4)=3. We cannot have a(4)=9, because b(3)=5 implies a(5)=3, and b(4)=|a(5)-a(4)|=6 which contradicts b(4)=3 as implied by a(3)=4. Therefore a(4)=10 is the smallest value of a(4) which will not generate a contradiction.
Crossrefs
Cf. A180428 - Inverse Permutation of this sequence. Also the first differences (absolute value) of this sequence.