cp's OEIS Frontend

A376306 Run-lengths of the sequence of first differences of squarefree numbers.

%I A376306 #9 Sep 21 2024 19:19:19
%S A376306 2,1,2,1,1,1,2,3,2,2,2,1,2,1,2,1,2,1,1,1,3,2,1,1,1,2,1,2,1,1,1,2,1,1,
%T A376306 1,2,3,2,1,1,2,1,2,1,2,1,2,1,1,1,1,1,1,2,1,1,1,2,1,2,1,1,1,1,1,1,1,2,
%U A376306 3,2,2,1,1,2,1,2,1,2,1,1,1,2,3,2,1,1,1
%N A376306 Run-lengths of the sequence of first differences of squarefree numbers.
%e A376306 The sequence of squarefree numbers (A005117) is:
%e A376306   1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, ...
%e A376306 The sequence of first differences (A076259) of squarefree numbers is:
%e A376306   1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 2, 2, 2, 1, 1, 3, 3, 1, 1, 2, 1, 1, 2, 1, ...
%e A376306 with runs:
%e A376306   (1,1),(2),(1,1),(3),(1),(2),(1,1),(2,2,2),(1,1),(3,3),(1,1),(2),(1,1), ...
%e A376306 with lengths A376306 (this sequence).
%t A376306 Length/@Split[Differences[Select[Range[100],SquareFreeQ]]]
%Y A376306 Run-lengths of first differences of A005117.
%Y A376306 Before taking run-lengths we had A076259, ones A375927.
%Y A376306 For prime instead of squarefree numbers we have A333254.
%Y A376306 For compression instead of run-lengths we have A376305.
%Y A376306 For run-sums instead of run-lengths we have A376307.
%Y A376306 For prime-powers instead of squarefree numbers we have A376309.
%Y A376306 For positions of first appearances instead of run-lengths we have A376311.
%Y A376306 A000040 lists the prime numbers, differences A001223.
%Y A376306 A000961 and A246655 list prime-powers, first differences A057820.
%Y A376306 A003242 counts compressed or anti-run compositions, ranks A333489.
%Y A376306 A005117 lists squarefree numbers, differences A076259.
%Y A376306 A013929 lists nonsquarefree numbers, differences A078147.
%Y A376306 A116861 counts partitions by compressed sum, by compressed length A116608.
%Y A376306 A274174 counts contiguous compositions, ranks A374249.
%Y A376306 Cf. A007674, A053797, A053806, A061398, A072284, A112925, A112926, A120992, A373198, A375707, A376312.
%K A376306 nonn
%O A376306 1,1
%A A376306 _Gus Wiseman_, Sep 21 2024