A104513 The number of consecutive integers > 1 beginning with A104512(n), the sum of which equals n, or 0 if impossible.

0, 0, 2, 0, 2, 3, 2, 0, 3, 4, 2, 3, 2, 4, 5, 0, 2, 4, 2, 5, 6, 4, 2, 3, 5, 4, 6, 7, 2, 5, 2, 0, 6, 4, 7, 8, 2, 4, 6, 5, 2, 7, 2, 8, 9, 4, 2, 3, 7, 5, 6, 8, 2, 9, 10, 7, 6, 4, 2, 8, 2, 4, 9, 0, 10, 11, 2, 8, 6, 7, 2, 9, 2, 4, 10, 8, 11, 12, 2, 5, 9, 4, 2, 8, 10, 4, 6, 11, 2, 12, 13, 8, 6, 4, 10, 3, 2, 7, 11, 8

Offset

1,3

References

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..16416

Formula

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

Example

a(18) = 4 because 3+4+5+6 = 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]; Length[ lst[[ Position[ Plus @@@ lst, n, 1, 1][[1, 1]]] ]]]]; Table[ f[n], {n, 100}]

Prog

(PARI) A104513(n) = if(!bitand(n, n-1), 0, my(b, d, u=1+sqrtint(2*n)); for(k=0, n-2, b = binomial(k+1, 2); forstep(j=min(n, k+u), k+2, -1, d = binomial(j+1, 2) - b; if(d==n, return(j-k), if(d<n, break)))); (0)); \\ Antti Karttunen, Mar 30 2021

Crossrefs

Cf. A104512, A104514, A104515, A104516.

Sequence in context: A246650 A264940 A272800 * A357618 A305610 A220455

Adjacent sequences: A104510 A104511 A104512 * A104514 A104515 A104516

Keyword

nonn,look

Author

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

Status

approved