This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A084760 #15 Sep 03 2021 06:54:28 %S A084760 2,3,5,10,13,17,23,30,38,47,57,69,82,93,107,122,138,155,173,193,214, %T A084760 233,255,278,302,327,353,381,410,437,467,498,530,563,597,633,670,705, %U A084760 743,782,822,863,905,949,994,1037,1085,1131,1178,1227,1277,1329,1382,1433 %N A084760 Squarefree numbers in ascending order such that the difference of successive terms is unique. a(m) - a(m-1) = a(k) - a(k-1) iff m = k. %C A084760 The sequence of first differences is 1, 2, 5, 3, 4, 6, 7, 8, 9, 10, 12, 13, 11, 14, 15, 16, 17, 18, 20, 21, 19, ... Conjecture: (1) every number is a term of this sequence. For every number r there exists some k such that a(k) - a(k-1) = r. Question: What is the longest string of consecutive integers in this sequence (of successive differences)? %C A084760 Answer: 5, as exemplified by the 6 values 17 to 57. Any longer series with differences consecutive integers must include a multiple of 4, as can be seen by enumerating all possibilities modulo 4. - _Franklin T. Adams-Watters_, Jul 14 2006 %e A084760 After 5 the next term is 10 and not 6 or 7, as 6-5 = 3-2 =1 and 7-5 = 5-3 = 2. %Y A084760 Cf. A005117, A084758, A084759. %K A084760 nonn %O A084760 1,1 %A A084760 _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 17 2003 %E A084760 More terms from _Franklin T. Adams-Watters_, Jul 14 2006