A104516 a(n) is the first occurrence of k in A104515, the difference between the maximum number of consecutive integers and the minimum number >1 of consecutive integers, the sum of which equals n.

1, 9, 30, 15, 21, 35, 54, 45, 55, 77, 156, 91, 105, 135, 204, 153, 171, 209, 252, 231, 253, 299, 450, 325, 351, 405, 522, 435, 465, 527, 594, 561, 595, 665, 888, 703, 741, 819, 984, 861, 903, 989

Offset

0,2

Comments

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

Where a(n)=k & a(n+2)=k+1 for k=54,252,594,...

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=0..41.

Example

a(2)=30 because 4+5+6+7+8 = 9+10+11 = 30.

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]]]; t = Table[0, {50}]; Do[ c = f[n]; If[ t[[c + 1]] == 0, t[[c + 1]] = n; Print[{n, c}]], {n, 10^4}]; t

Crossrefs

Cf. A104512, A104513, A104514, A104515.

Sequence in context: A173262 A337445 A291159 * A279618 A158503 A179506

Adjacent sequences: A104513 A104514 A104515 * A104517 A104518 A104519

Keyword

nonn

Author

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

Status

approved