MathDB

find a term of a sequence

Source: Ireland 1999

July 4, 2009

inductionnumber theory proposednumber theory

Problem Statement

The sequence

u_n

, n\equal{}0,1,2,... is defined by u_0\equal{}0, u_1\equal{}1 and for each

n \ge 1

, u_{n\plus{}1} is the smallest positive integer greater than

u_n

such that \{ u_0,u_1,...,u_{n\plus{}1} \} contains no three elements in arithmetic progression. Find

u_{100}