Search: id:A066510 Results 1-1 of 1 results found. %I A066510 %S A066510 6,14,34,42,58,62,66,70,78,86,90,102,110,114,130,158,178,182,202, %T A066510 210,230,238,254,258,266,274,278,302,306,310,314,322,326,330,358, %U A066510 374,378,390,394,398,402,410,418,422,426,430,434,438,446,450,454 %N A066510 Conjectured list of positive numbers which are not of the form r^i-s^j, where r,s,i,j are integers with i>1, j>1. %C A066510 This is a famous hard problem and the terms shown are only conjectured values. %C A066510 The terms shown are not the difference of two powers below 10^19. - Don Reble. %C A066510 One can immediately represent the odd numbers and the multiples of four as differences of two squares. - Don Reble. %D A066510 R. K. Guy, Unsolved Problems in Number Theory, Sections D9 and B19. %H A066510 Alf van der Poorten, Remarks on the sequence of 'perfect' powers %e A066510 Examples showing that certain numbers are not in the sequence: 10 = 13^3-3^7, 22 = 7^2 - 3^3, 29 = 15^2 - 14^2, 31 = 2^5 - 1, 52 = 14^2 - 12^2, 54 = 3^4 - 3^3, 60 = 2^6 - 2^2, 68 = 10^2 - 2^5, 72 = 3^4 - 3^2, 76 = 5^3 - 7^2, 84 = 10^2 - 2^4, ... %e A066510 50 = 7^2 - -1^3, 82 = 9^2 - -1^3, 226 = 15^2 - -1^3, 246 = 11^2 - -5^3, 290 = 17^2 - -1^3, ... [Typos corrected by Gerry Myerson (gerry(AT)math.mq.edu.au), May 14 2008] %Y A066510 Cf. A074980, A023057. %Y A066510 Sequence in context: A078836 A142875 A074981 this_sequence A036387 A053560 A119874 %Y A066510 Adjacent sequences: A066507 A066508 A066509 this_sequence A066511 A066512 A066513 %K A066510 nonn,hard %O A066510 1,1 %A A066510 Don Reble (djr(AT)nk.ca), Oct 12 2002 Search completed in 0.001 seconds