A163169 a(n) = minimal number of consecutive integers required which when summed make n.

0, 2, 0, 2, 0, 2, 3, 2, 0, 2, 4, 2, 3, 2, 4, 2, 0, 2, 3, 2, 5, 2, 4, 2, 3, 2, 4, 2, 7, 2, 3, 2, 0, 2, 4, 2, 3, 2, 4, 2, 5, 2, 3, 2, 8, 2, 4, 2, 3, 2, 4, 2, 8, 2, 3, 2, 7, 2, 4, 2, 3, 2, 4, 2, 0, 2, 3, 2, 8, 2, 4, 2, 3, 2, 4, 2, 8, 2, 3, 2, 5, 2, 4, 2, 3, 2, 4, 2, 11, 2, 3, 2, 8, 2, 4, 2, 3, 2, 4, 2, 5, 2, 3, 2

Offset: 0

Author

Carl R. White, Jul 22 2009

Keywords

• easy
• nonn

Comments

Zeros occur where no number of consecutive integers can be summed to make n; This only happens where n is an even power of two, or zero itself.

Entries where this sequence is nonzero are in A138591.

Examples

			20 = 2 + 3 + 4 + 5 + 6; No shorter sequence of consecutive integers sums to 20 and so a(20) = the number of elements in {2,3,4,5,6} = 5.
15 = 4 + 5 + 6, but also 15 = 7 + 8, so a(15) = 2, since this is the minimum.
		

Links

• Ray Chandler, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A138591, A057716.