cp's OEIS Frontend

A309783 Numbers that are sums of one or more consecutive positive triangular numbers in more than one way.

%I A309783 #18 Aug 21 2019 16:16:23
%S A309783 10,36,55,64,100,120,136,164,210,276,361,435,460,514,560,596,676,760,
%T A309783 1176,1225,1320,1326,1460,1484,1485,1505,1540,1684,1736,1770,1891,
%U A309783 1936,2014,2080,2145,2180,2314,2485,2596,2890,3156,3244,3275,3364,3486,3570,3710,3916
%N A309783 Numbers that are sums of one or more consecutive positive triangular numbers in more than one way.
%C A309783 The first number that is the sum in three ways is 2180. The first that is the sum in four ways is 10053736. - _Robert Israel_, Aug 20 2019
%H A309783 Chai Wah Wu, <a href="/A309783/b309783.txt">Table of n, a(n) for n = 1..10000</a> (first 2759 terms from Robert Israel)
%F A309783 A307666(a(n)) > 1.
%p A309783 N:= 10000: # for terms <= N
%p A309783 V:= Vector(N):
%p A309783 for i from 1 while i*(i+1)/2 <= N do
%p A309783   s:= i*(i+1)*(i+2)/6;
%p A309783   for j from i-1 to 0 by -1 do
%p A309783     t:= j*(j+1)*(j+2)/6;
%p A309783     if s-t > N then break fi;
%p A309783     V[s-t]:= V[s-t]+1
%p A309783   od;
%p A309783 od:
%p A309783 select(t -> V[t]>1, [$1..N]); # _Robert Israel_, Aug 20 2019
%Y A309783 Cf. A000217, A034706, A130052, A307666.
%K A309783 nonn
%O A309783 1,1
%A A309783 _Ilya Gutkovskiy_, Aug 17 2019