Answer
procedure maxsum $( a_1, a_2, a_3, ... a_n:$ a sequence of integers $)$
currentsum $:= a_1$
Initialize a list RESULT to contain all values $\alpha$ such that $a_{\alpha}>\sum_{i = 1}^{\alpha-1} a_i$
for $m :=2$ to $n$
$\space\space\space$ if $a_m>$ currentsum then add $a_m$ to RESULT
$\space\space\space$ currentsum $:= $ currentsum $+ a_m$
return RESULT
Work Step by Step
This algorithm attempts to find the set of integers such that they are greater than the sum of the previous terms. It does this by comparing each integer to the sum attained to the point; adding it to the result set if it satisfies the condition and then updating the sum as required.
