A368485 Lexicographically earliest infinite sequence of positive integers such that for n > 1, a(n - a(n)) is distinct for all indices n with the same a(n) value.

1, 1, 2, 1, 2, 3, 1, 2, 3, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 4, 4, 5, 6, 1, 2, 3, 4, 5, 5, 5, 6, 7, 1, 2, 3, 4, 5, 6, 6, 7, 8, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 6, 6, 6, 7, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 7, 7, 7, 8, 8, 9, 10, 11

Offset

1,3

Comments

Consider each index i as a location from which one can jump a(i) terms backwards. Any two distinct indices m and k, where a(m)=a(k), will jump to distinct values. In other words, every 1 will jump back to a distinct value, every 2, 3, etc.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program

Example

We can see, for example, that the values reached by jumping backwards once from each 3 in the sequence are all distinct:
  1, 1, 2, 1, 2, 3, 1, 2, 3, 3, 4, 1, 2, 3, 4, 5, 1, 2, 3
        2<=======*
                 3<=======*
                    1<=======*  4<=======*     5<=======*

Prog

(PARI) See Links section.

Crossrefs

Cf. A367849, A367832, A367467.

Sequence in context: A115452 A039676 A242359 * A113126 A348043 A138060

Adjacent sequences: A368482 A368483 A368484 * A368486 A368487 A368488

Keyword

nonn

Author

Neal Gersh Tolunsky, Dec 28 2023

Extensions

More terms from Rémy Sigrist, Jan 15 2024

Status

approved