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.
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
KEYWORD
nonn
AUTHOR
Alfred S. Posamentier (asp2(AT)juno.com) and Robert G. Wilson v, Feb 23 2005
STATUS
approved