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

1,15

Comments

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

References

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

Links

Table of n, a(n) for n=1..104.

Example

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

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}]

Crossrefs

Cf. A104512, A104513, A104514, A104516.

Sequence in context: A174903 A167163 A005890 * A337923 A363880 A324874

Adjacent sequences: A104512 A104513 A104514 * A104516 A104517 A104518

Keyword

nonn

Author

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

Status

approved