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

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, 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, 3, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 3, 2, 1, 1, 1

Offset: 1

Author

Gus Wiseman, Sep 21 2024

Keywords

• nonn

Examples

			The sequence of squarefree numbers (A005117) is:
  1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, ...
The sequence of first differences (A076259) of squarefree numbers is:
  1, 1, 2, 1, 1, 3, 1, 2, 1, 1, 2, 2, 2, 1, 1, 3, 3, 1, 1, 2, 1, 1, 2, 1, ...
with runs:
  (1,1),(2),(1,1),(3),(1),(2),(1,1),(2,2,2),(1,1),(3,3),(1,1),(2),(1,1), ...
with lengths A376306 (this sequence).
		

Crossrefs

Run-lengths of first differences of A005117.

Before taking run-lengths we had A076259, ones A375927.

For prime instead of squarefree numbers we have A333254.

For compression instead of run-lengths we have A376305.

For run-sums instead of run-lengths we have A376307.

For prime-powers instead of squarefree numbers we have A376309.

For positions of first appearances instead of run-lengths we have A376311.

A000040 lists the prime numbers, differences A001223.

A000961 and A246655 list prime-powers, first differences A057820.

A003242 counts compressed or anti-run compositions, ranks A333489.

A005117 lists squarefree numbers, differences A076259.

A013929 lists nonsquarefree numbers, differences A078147.

A116861 counts partitions by compressed sum, by compressed length A116608.

A274174 counts contiguous compositions, ranks A374249.

Cf. A007674, A053797, A053806, A061398, A072284, A112925, A112926, A120992, A373198, A375707, A376312.

Programs

Mathematica

Length/@Split[Differences[Select[Range[100],SquareFreeQ]]]