A104512 a(n) is the minimum number that is the first of k > 1 consecutive integers whose sum equals n, or 0 if impossible.

0, 0, 1, 0, 2, 1, 3, 0, 2, 1, 5, 3, 6, 2, 1, 0, 8, 3, 9, 2, 1, 4, 11, 7, 3, 5, 2, 1, 14, 4, 15, 0, 3, 7, 2, 1, 18, 8, 4, 6, 20, 3, 21, 2, 1, 10, 23, 15, 4, 8, 6, 3, 26, 2, 1, 5, 7, 13, 29, 4, 30, 14, 3, 0, 2, 1, 33, 5, 9, 7, 35, 4, 36, 17, 3, 6, 2, 1, 39, 14, 5, 19, 41, 7, 4, 20, 12, 3, 44, 2, 1, 8, 13

Offset: 1

Author

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

Keywords

• nonn
• look

Examples

			a(18) = 3 because 3+4+5+6 = 5+6+7 = 18 but 3 < 5.
		

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

Crossrefs

Cf. A104513, A104514, A104515, A104516.

Cf. A118235.

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]; lst[[ Position[ Plus @@@ lst, n, 1, 1][[1, 1]], 1]]]]; Table[ f[n], {n, 93}] (* Robert G. Wilson v, Feb 25 2005 *)

PARI

A104512(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(1+k),if(dAntti Karttunen, Mar 30 2021

Formula

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

a(n)=1 iff n is a triangular number (A000217).