Track / Stage 4 / 215 of 340 #475 of 1964

Problem 475

AMC 12 late, AIME early

Number theory Difficulty 4.9 Find the answer

Find the law that forms the sequence and give its next 2 terms:

$425,470,535,594,716,802, \ldots$

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Official solution

Each term is the sum of the previous term and the squares of each of its digits:

$470=425+4^{2}+2^{2}+5^{2}, 535=470+4^{2}+7^{2}+0^{2}, \ldots$

Thus, the next terms are: 870 and 983.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.