sequence number theory sequence sequence member sequence product previous members plus terms sequence sequence sequence named investigated values grow sum forms series unit rapidly series unit number terms defined allows numbers sequence easily numbers magnitude rapid growth sequence complete prime known members values derived sequence construct finite egyptian fraction representations hard instances online formal definitions formally sequence defined formula formula product set alternatively define sequence formula straightforward induction equivalent definition closed form formula numbers grow function specifically shown formula number approximately formula effect following nearest nearest nearest square times nearest practical better way calculating number places calculating taking repeated square root double growth sequence compares sequence numbers numbers usually defined formula formula defined product formula similar defining sequence formula connection egyptian unit formed values sequence generate infinite series formula partial sums series simple form formula proved induction directly noting implies formula sum formula sequence partial sums overall series forms infinite egyptian fraction representation number formula find finite egyptian fraction representations length series formula sum terms infinite series provides closest possible term egyptian fraction example terms add egyptian fraction number open interval requires terms possible interpret sequence result egyptian step chooses smallest possible makes partial sum series alternatively terms sequence viewed odd expansion quickly growing series rational sums observed sequence unique having quickly growing values simultaneously having series rational number sequence provides example showing double growth cause sequence sequence precise follows results sequence formula grows quickly formula series formula rational number point sequence defined formula define sequence results type inequality growth sequence replaced weaker condition formula surveys progress related brown follows definition numbers sequence relatively prime sequence prove infinitely prime numbers prime divide number sequence strongly prime factor number sequence sequence prove infinitely remains unknown numbers sequence instance known numbers sequence known terms describes easy determine number given prime divides simply defining numbers finding number zero finding repeated technique found million numbers square divides number set occur factors numbers density zero set number formula following table shows known numbers prime customary denote prime composite numbers long applications use properties sequence define large numbers having differential odd dimensional spheres exotic spheres number distinct sphere dimension proportional double growth describe brown values derived sequence construct lower bound examples online packing similarly use sequence lower bound performance dimensional cutting stock problem concerns sets numbers number set divides equal product numbers plus inequality requirement values sequence solve problem requirement solutions derived similar defining sequence solutions problem applications classification surface hill theory finite describes application closest term sums unit lower number perfect number miller uses property lower bound size certain groups
Sylvester's sequence