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

Author

Neal Gersh Tolunsky, Dec 28 2023

Keywords

• nonn

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.

Examples

			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<=======*
		

Links

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

Crossrefs

Cf. A367849, A367832, A367467.

Programs

PARI

See Links section.

Extensions

More terms from Rémy Sigrist, Jan 15 2024