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 A376312 #9 Sep 25 2024 09:59:47 %S A376312 4,1,3,4,2,4,1,2,1,4,1,3,1,2,4,3,1,4,3,1,4,1,3,4,2,4,2,1,4,1,3,1,3,1, %T A376312 2,4,3,1,4,3,1,2,1,3,4,2,4,1,2,1,3,1,4,1,3,4,2,4,3,1,4,1,3,4,2,4,2,1, %U A376312 3,2,4,1,3,4,2,3,1,3,1,4,1,3,2,1,3,4,2 %N A376312 Run-compression of first differences (A078147) of nonsquarefree numbers (A013929). %C A376312 We define the run-compression of a sequence to be the anti-run obtained by reducing each run of repeated parts to a single part. Alternatively, we can remove all parts equal to the part immediately to their left. For example, (1,1,2,2,1) has run-compression (1,2,1). %e A376312 The sequence of nonsquarefree numbers (A013929) is: %e A376312 4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, 32, 36, 40, 44, 45, 48, 49, 50, ... %e A376312 with first differences (A078147): %e A376312 4, 1, 3, 4, 2, 2, 4, 1, 2, 1, 4, 4, 4, 4, 1, 3, 1, 1, 2, 2, 2, 4, 3, 1, ... %e A376312 with runs: %e A376312 (4),(1),(3),(4),(2,2),(4),(1),(2),(1),(4,4,4,4),(1),(3),(1,1),(2,2,2), ... %e A376312 and run-compression (A376312): %e A376312 4, 1, 3, 4, 2, 4, 1, 2, 1, 4, 1, 3, 1, 2, 4, 3, 1, 4, 3, 1, 4, 1, 3, 4, ... %t A376312 First/@Split[Differences[Select[Range[100], !SquareFreeQ[#]&]]] %Y A376312 For nonprime instead of squarefree numbers we have A037201, halved A373947. %Y A376312 Before compressing we had A078147. %Y A376312 For run-sums instead of compression we have A376264. %Y A376312 For squarefree instead of nonsquarefree we have A376305, ones A376342. %Y A376312 For prime-powers instead of nonsquarefree numbers we have A376308. %Y A376312 A000040 lists the prime numbers, differences A001223. %Y A376312 A000961 and A246655 list prime-powers, differences A057820. %Y A376312 A003242 counts compressed compositions, ranks A333489. %Y A376312 A005117 lists squarefree numbers, differences A076259 (ones A375927). %Y A376312 A013929 lists nonsquarefree numbers, differences A078147. %Y A376312 A116861 counts partitions by compressed sum, by compressed length A116608. %Y A376312 Cf. A007674, A053797, A053806, A072284, A112925, A120992, A274174, A373198, A375707, A376306, A376307, A376311. %K A376312 nonn %O A376312 1,1 %A A376312 _Gus Wiseman_, Sep 24 2024