proposed

approved

editing

proposed

Cf. A005117, A006560, A006562, A029707, A037201, A038664, A069010, A076259, A176246.

For composite runs: A005381, A006093, A008864, A054265, A068780, A176246, A373403, A373404.

Cf. A005117, A006560, A006562, A029707, A037201, A038664, A069010, A076259, A176246.

Run-lengths of A251092.

The runs of odd primes differing by 2 begin:

3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, ...

with runs:

with lengths:

with lengths 3, 2, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, ..., which have runs beginning:

which have runs beginning:

For antiruns we have A373820, run-lengths of A027833 (partial sums A029707if we prepend 1).

A005117 lists the squarefree numbers, first differences A076259.

For prime runs see: A001359, A006512, A025584, A067774, A373405, A373406.

For composite runs see: A005381, A006093, A008864, A054265, A068780, A176246, A373403, A373404.

Cf. A005117, A006560, A006562, A029707, A037201, A038664, ~A061398, `A069010, `A073051, `A122535, ~A371201A076259.

Cf. A006560, A006562, A037201, A038664, ~A061398, `A069010, `A073051, ~A112925, ~A112926, `A122535, ~A174965, ~A350842, ~A371201, ~A373197.

Differences of consecutive primes are A001223, run-lengths A333254, run-lengths of run-lengths A373821.

A000040 lists the primes, differences A001223.

A001223 gives differences of consecutive primes, run-lengths A333254, run-lengths of run-lengths A373821.

For prime runs see : A001359, A006512, A025584, A067774, A373405, A373406.

For composite runs see : A005381, A006093, A008864, A054265, A068780, A176246, A373403, A373404.

allocated for Gus WisemanRun-lengths (differing by 0) of the run-lengths (differing by 2) of the odd primes.

1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 3, 2, 4, 3, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 3, 1, 10, 2, 4, 1, 7, 1, 4, 1, 3, 1, 2, 1, 1, 1, 2, 1, 18, 3, 2, 1, 2, 1, 17, 2, 1, 2, 2, 1, 6, 1, 9, 1, 3, 1, 1, 1, 1, 1, 1, 1, 8, 1, 3, 1, 2, 2, 15, 1, 1, 1, 4, 1, 1, 1, 1, 1, 7, 1

1,2

Gus Wiseman, <a href="/A373403/a373403.txt">Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers</a>.

The runs of odd primes differing by 2 begin:

3 5 7

11 13

17 19

23

29 31

37

41 43

47

53

59 61

67

71 73

with lengths 3, 2, 2, 1, 2, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 2, 2, ..., which have runs beginning:

3

2 2

1

2

1

2

1 1

2

1

2

1 1 1 1

2 2

1 1 1

with lengths a(n).

Length/@Split[Length/@Split[Select[Range[3, 1000], PrimeQ], #1+2==#2&]//Most]//Most

Differences of consecutive primes are A001223, run-lengths A333254, run-lengths of run-lengths A373821.

Run-lengths of A251092.

For antiruns we have A373820, run-lengths of A027833 (partial sums A029707).

Positions of first appearances are A373825, sorted A373824.

A000040 lists the primes, differences A001223.

A005117 lists the squarefree numbers, first differences A076259.

A046933 counts composite numbers between primes.

A065855 counts composite numbers up to n.

A071148 gives partial sums of odd primes.

For prime runs see A001359, A006512, A025584, A067774, A373405, A373406.

For composite runs see A005381, A006093, A008864, A054265, A068780, A176246, A373403, A373404.

Cf. A006560, A006562, A037201, A038664, ~A061398, `A069010, `A073051, ~A112925, ~A112926, `A122535, ~A174965, ~A350842, ~A371201, ~A373197.

allocated

nonn

Gus Wiseman, Jun 20 2024

approved

editing

allocated for Gus Wiseman

allocated

approved