A110351 Least sum (n+1) + (n+2) + ... + (n+k) that is a multiple of the n-th triangular number, n(n+1)/2.

2, 3, 30, 110, 30, 84, 1148, 1980, 585, 935, 462, 702, 2912, 105, 3120, 32504, 9027, 11457, 2660, 420, 2772, 26312, 16560, 19800, 44525, 52299, 17388, 20300, 10005, 11625, 460784, 61248, 11220, 2975, 24570, 43290, 220742, 29640, 4680, 188600

Offset

1,1

Links

Paolo P. Lava, Table of n, a(n) for n = 1..250

Example

a(3) = 4 + 5 + 6 + 7 + 8 = 30 = 5*6, T(3) = 3*4/2 = 6.

Maple

a:=proc(n) local p, m: p:=proc(k) if type(sum(n+j, j=1..k)/(n*(n+1)/2), integer)=true then k else fi end: m:=[seq(p(k), k=1..1200)][1]: sum(n+j, j=1..m) end: seq(a(n), n=1..45); # Emeric Deutsch, Aug 08 2005

Mathematica

Do[t = n*(n+1)/2; k = 1; While[Mod[k*n + k*(k+1)/2, t] > 0, k++ ]; Print[k*n + k*(k+1)/2], {n, 1, 50}] (* Ryan Propper, Aug 08 2005  *)

Crossrefs

Cf. A000217, A110352, A110353.

Sequence in context: A325506 A203431 A137981 * A326224 A270483 A217370

Adjacent sequences: A110348 A110349 A110350 * A110352 A110353 A110354

Keyword

nonn

Author

Amarnath Murthy, Jul 21 2005

Extensions

More terms from Emeric Deutsch and Ryan Propper, Aug 08 2005

Status

approved