8

Part of 2011 Ukraine Team Selection Test

Problems(1)

any natural number can be given as a_i+a_j, a _n>n^2 /16, increasing

Source: Ukraine TST 2011 p8

Is there an increasing sequence of integers

0 = {{a} _{0}} <{{a} _{1}} <{{a} _{2}} <\ldots

for which the following two conditions are satisfied simultaneously: 1) any natural number can be given as

{{a} _{i}} + {{a} _{j}}

for some (possibly equal)

i \ge 0

j \ge 0

{{a} _ {n}}> \tfrac {{{n} ^ {2}}} {16}

for all natural

n

SequencealgebraNatural Numbers