▁have ▁sizes ▁that ▁are ▁consecutive ▁F ib on acci ▁numbers . ▁On ▁average , ▁this ▁leads ▁to ▁about ▁ 4 % ▁more ▁compar isons ▁to ▁be ▁executed , ▁but ▁it ▁has ▁the ▁advantage ▁that ▁one ▁only ▁needs ▁addition ▁and ▁sub tra ction ▁to ▁calculate ▁the ▁indices ▁of ▁the ▁accessed ▁array ▁elements , ▁while ▁classical ▁binary ▁search ▁needs ▁bit - shift , ▁division ▁or ▁multiplication , ▁operations ▁that ▁were ▁less ▁common ▁at ▁the ▁time ▁F ib on acci ▁search ▁was ▁first ▁published . ▁F ib on acci ▁search ▁has ▁an ▁average - ▁and ▁worst - case ▁complexity ▁of ▁O ( log ▁n ) ▁( see ▁Big ▁O ▁notation ). ▁ ▁The ▁F ib on acci ▁sequence ▁has ▁the ▁property ▁that ▁a ▁number ▁is ▁the ▁sum ▁of ▁its ▁two ▁prede cess ors . ▁Therefore ▁the ▁sequence ▁can ▁be ▁computed ▁by ▁repeated ▁addition . ▁The ▁ratio ▁of ▁two ▁consecutive ▁numbers ▁approaches ▁the ▁Golden ▁ratio , ▁ 1 . 6 1 8 ... ▁Binary ▁search ▁works ▁by ▁div iding ▁the ▁seek ▁area ▁in ▁equal ▁parts ▁( 1 : 1 ). ▁F ib on acci ▁search ▁can ▁divide ▁it ▁into ▁parts ▁approaching ▁ 1 : 1 . 6 1 8 ▁while ▁using ▁the ▁simpler ▁operations . ▁ ▁If ▁the ▁elements ▁being ▁searched ▁have ▁non - uniform ▁access ▁memory ▁storage ▁( i . ▁e ., ▁the ▁time ▁needed ▁to ▁access ▁a ▁storage ▁location ▁var ies ▁depending ▁on ▁the ▁location ▁accessed ), ▁the ▁F ib on acci ▁search ▁may ▁have ▁the ▁advantage ▁over ▁binary ▁search ▁in ▁slightly ▁reducing ▁the ▁average