%I A075772
%S A075772 3,3,1,1,7,2,2,4,4,13,15,17,19,4,3,3,16,25,20,9,9,13,13,33,19,18,18,39,
%T A075772 41,28,17,17,47,49,51,53,55,57,59,39,24,24,65,67,69,35,35,38,75,77,79,
%U A075772 47,36,36,85,87,23,23,68,10,10,12,95,97,99,101,40,40,65,107,100,11,11
%N A075772 Difference between n-th perfect power and the closest perfect power.
%C A075772 Let {b(n)} be the sequence of perfect powers (A001597); then a(n) = min 
               { b(n)-b(n-1), b(n+1)-b(n) }.
%e A075772 The perfect powers are 1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 100, 
               121, etc. The 7th is 27. This is 2 larger than the 6th (25) and 5 
               smaller than the 8th (32). So a(7)=2.
%t A075772 pp = {-2, 1}; Do[ If[ !PrimeQ[n] && Apply[GCD, Last[ Transpose[ FactorInteger[n]]]] 
               > 1, pp = Append[pp, n]], {n, 2, 10^4}]; Table[ Min[pp[[n + 1]] - 
               pp[[n]], pp[[n + 2]] - pp[[n + 1]]], {n, 1, 75}]
%Y A075772 Cf. A001597, A053289, A075773.
%Y A075772 Sequence in context: A083029 A084546 A026515 this_sequence A142157 A119608 
               A101842
%Y A075772 Adjacent sequences: A075769 A075770 A075771 this_sequence A075773 A075774 
               A075775
%K A075772 nonn
%O A075772 1,1
%A A075772 N. Fernandez (primeness(AT)borve.org), Oct 09 2002
%E A075772 More terms from Robert G. Wilson v (rgwv(AT)rgwv.com) and John W. Layman 
               (layman(AT)math.vt.edu), Oct 10 2002