Search: id:A140074 Results 1-1 of 1 results found. %I A140074 %S A140074 1,1,1,0,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,1,0,1,1, %T A140074 0,1,0,0,0,1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0, %U A140074 1,0,1,1,1,1,0,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,1 %N A140074 Excess over the asymptote of the number of perfect squares between cubes. %C A140074 There are always at least two squares between positive consecutive cubes, starting with the perfect squares 1 and 4 between the perfect cubes 1 (included) and 8 (excluded). %C A140074 The number of squares between the cube of n (included) and the cube of n+1 (excluded) is always one of the two integers bracketing 3*sqrt(n)/ 2. %C A140074 The number a(n) in the sequence is 0 if the correct count is the lower number or 1 if the actual count is the higher number. %H A140074 G. P. Michon, A Sequence of Bits with Strange Statistics. %F A140074 a(n) = floor(sqrt((n+1)^3-1)) - ceiling(sqrt(n^3)) + 1 - floor(1.5 sqrt(n)) %e A140074 The sequence starts with a(0)=1 for n=0 because there is just one perfect square (0) between the cube of 0 (included) and the cube of 1 (excluded). %e A140074 This exceeds by a(0)=1 the asymptotic expression floor(1.5*sqrt(n)) for the value n=0. %Y A140074 Sequence in context: A092079 A139312 A071041 this_sequence A090174 A165556 A127243 %Y A140074 Adjacent sequences: A140071 A140072 A140073 this_sequence A140075 A140076 A140077 %K A140074 easy,nonn %O A140074 0,1 %A A140074 Gerard P. Michon (g.michon(AT)att.net), May 06 2008 Search completed in 0.001 seconds