A104515 Difference between the maximum number of consecutive integers and the least number >1 of consecutive integers, the sum of which equals 2n.

0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 1, 0, 0, 4, 0, 0, 0, 3, 0, 4, 0, 0, 2, 0, 0, 4, 0, 5, 5, 0, 0, 4, 0, 0, 4, 0, 0, 7, 0, 0, 0, 5, 1, 4, 0, 0, 6, 8, 0, 4, 0, 0, 5, 0, 0, 7, 0, 8, 8, 0, 0, 4, 3, 0, 6, 0, 0, 8, 0, 9, 9, 0, 0, 7, 0, 0, 5, 8, 0, 4, 0, 0, 9, 11, 0, 4, 0, 8, 0, 0, 3, 9, 3, 0, 9, 0, 0

Offset: 1

Author

Alfred S. Posamentier (asp2(AT)juno.com) and Robert G. Wilson v, Feb 23 2005

Keywords

• nonn

Comments

a(n)=0 iff n=2^k.

Examples

			a(18) = 1 because 3+4+5+6 = 5+6+7 = 18.
		

References

• Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, page 67.

Crossrefs

Cf. A104512, A104513, A104514, A104516.

Programs

Mathematica

f[n_] := Block[{r = Ceiling[n/2]}, If[ IntegerQ[ Log[2, n]], 0, m = Range[r]; lst = Flatten[ Table[ m[[k]], {i, r}, {j, i + 1, r}, {k, i, j}], 1]; l = Length /@ lst[[ Flatten[ Position[ Plus @@@ lst, n]]]]; Max[l] - Min[l]]]; Table[ f[2n], {n, 105}]