A357987 Lexicographically earliest sequence of positive integers such that no sum of consecutive terms is a square or higher power of an integer.

2, 3, 2, 5, 5, 2, 3, 2, 21, 5, 2, 5, 5, 5, 7, 6, 5, 6, 6, 7, 11, 24, 2, 13, 5, 6, 35, 7, 10, 34, 6, 15, 2, 28, 10, 2, 5, 14, 19, 2, 5, 28, 2, 3, 2, 35, 2, 18, 6, 11, 3, 3, 37, 2, 5, 26, 29, 33, 42, 13, 5, 5, 10, 11, 13, 21, 18, 5, 10, 5, 6, 7, 24, 20, 3, 15

Offset: 1

Author

Rémy Sigrist, Oct 23 2022

Keywords

• nonn

Comments

This sequence is a variant of A357579 where we allow duplicates.

This sequence is well defined as we have arbitrary large gaps in A001597.

Examples

			For n = 1:
- 2 is not a perfect power,
- so a(1) = 2.
For n = 2:
- 2 + 2 is a perfect power,
- neither 2 + 3 nor 3 are perfect powers,
- so a(2) = 3.
For n = 3:
- none of 2 + 3 + 2, 3 + 2, 2 is a perfect power,
- so a(3) = 2.
		

Links

• Rémy Sigrist, C program

Crossrefs

Cf. A001597, A007916, A357579.

Programs

C

See Links section.