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A110351 Least sum (n+1) + (n+2) + ... + (n+k) that is a multiple of the n-th triangular number, n(n+1)/2. 3

%I #13 Feb 04 2015 09:50:22

%S 2,3,30,110,30,84,1148,1980,585,935,462,702,2912,105,3120,32504,9027,

%T 11457,2660,420,2772,26312,16560,19800,44525,52299,17388,20300,10005,

%U 11625,460784,61248,11220,2975,24570,43290,220742,29640,4680,188600

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

%H Paolo P. Lava, <a href="/A110351/b110351.txt">Table of n, a(n) for n = 1..250</a>

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

%p 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

%t 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 *)

%Y Cf. A000217, A110352, A110353.

%K nonn

%O 1,1

%A _Amarnath Murthy_, Jul 21 2005

%E More terms from _Emeric Deutsch_ and _Ryan Propper_, Aug 08 2005

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