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

0,2

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

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 *)

Crossrefs

Cf. A121644 (strictly increasing version).

Sequence in context: A295165 A258023 A190232 * A276765 A121644 A259623

Adjacent sequences: A084690 A084691 A084692 * A084694 A084695 A084696

Keyword

nonn

Author

Amarnath Murthy, Jun 04 2003

Extensions

More terms from David Wasserman, Dec 30 2004

Status

approved