A084693 a(n) is smallest positive integer not already in the sequence such that every partial sum is squarefree.

1, 2, 3, 4, 5, 6, 8, 9, 13, 7, 11, 10, 12, 14, 17, 15, 18, 19, 16, 20, 21, 22, 24, 25, 27, 26, 28, 23, 29, 30, 32, 33, 31, 34, 36, 38, 37, 35, 40, 41, 39, 42, 43, 45, 46, 44, 48, 49, 51, 50, 47, 52, 55, 53, 56, 57, 54, 58, 59, 60, 61, 63, 64, 65, 62, 66, 67, 68, 69, 70, 72, 73

Offset: 0

Author

Amarnath Murthy, Jun 04 2003

Keywords

• nonn

Comments

Does every positive integer occur in the sequence?

The longest string of consecutive numbers is 6.

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A121644 (strictly increasing version).

Programs

Mathematica

a = {1}; Do[k = 1; While[Nand[! MemberQ[a, k], SquareFreeQ[Sum[a[[i]], {i, n}] + k]], k++]; AppendTo[a, k], {n, 71}]; a (* Michael De Vlieger, Sep 03 2015 *)

Extensions

More terms from David Wasserman, Dec 30 2004