Vyxal, 13 bytes
0?(»Þ'ZḆ»↜Œ∑∫»Þ([ǒ»Ȯİ∑Ṡ
A port of the 05AB1E answer
Explained
0?(»Þ'ZḆ»↜Œ∑∫»Þ([ǒ»Ȯİ∑Ṡ
0? # Push 0 followed by the input number
( # Input number of times:
»Þ'ZḆ»»Þ([ǒ» # Push the number 433544355
↜ŒȮİ # And get the indexes corresponding to the numbers in the second last item on the stack
∑∫∑Ṡ # Sum that list and then the stack