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

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.

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

Examples

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

References

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

Crossrefs

Cf. A104512, A104513, A104514, A104515.

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