A104514 a(n) = least number k > 1 of consecutive integers which sum to 2*n; or a(n) = 0 if n is a power of 2.

0, 0, 3, 0, 4, 3, 4, 0, 3, 5, 4, 3, 4, 7, 3, 0, 4, 3, 4, 5, 3, 8, 4, 3, 4, 8, 3, 7, 4, 3, 4, 0, 3, 8, 4, 3, 4, 8, 3, 5, 4, 3, 4, 11, 3, 8, 4, 3, 4, 5, 3, 13, 4, 3, 4, 7, 3, 8, 4, 3, 4, 8, 3, 0, 4, 3, 4, 16, 3, 5, 4, 3, 4, 8, 3, 16, 4, 3, 4, 5, 3, 8, 4, 3, 4, 8, 3, 11, 4, 3, 4, 16, 3, 8, 4, 3, 4, 7, 3, 5, 4, 3, 4

Offset

1,3

Comments

a(2^k) = 0 and a(3*n) = 3.

Least proper divisor d of 4*n (if any) such that d or 4*n/d is odd. - Robert Israel, May 06 2015

References

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

a(n) = A163169(2*n). Robert Israel, May 06 2015

Example

a(9) = 3 because 3+4+5+6 = 5+6+7 = 2*9 = 18.

Maple

a:= proc(n) local divs, r;
   divs:= select(t -> t::odd or (4*n/t)::odd, numtheory:-divisors(4*n) minus {1, 4*n});
   if nops(divs)=0 then 0 else min(divs) fi
end proc:
seq(a(n), n=1..200); # Robert Israel, May 06 2015

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]; Min[Length /@ lst[[Flatten[Position[Plus @@@ lst, n]]]]]]]; Table[f[2n], {n, 103}]

Crossrefs

Cf. A104512, A104513, A104515, A104516, A163169.

Sequence in context: A245907 A104686 A301428 * A349915 A072480 A243920

Adjacent sequences: A104511 A104512 A104513 * A104515 A104516 A104517

Keyword

nonn

Author

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

Status

approved