A373821 Run-lengths of run-lengths of first differences of odd primes.

1, 11, 1, 19, 1, 1, 1, 5, 1, 6, 1, 16, 1, 27, 1, 3, 1, 1, 1, 6, 1, 9, 1, 29, 1, 2, 1, 18, 1, 1, 1, 5, 1, 3, 1, 17, 1, 19, 1, 30, 1, 17, 1, 46, 1, 17, 1, 27, 1, 30, 1, 5, 1, 36, 1, 41, 1, 10, 1, 31, 1, 44, 1, 4, 1, 14, 1, 6, 1, 2, 1, 32, 1, 13, 1, 17, 1, 5

Offset: 1

Author

Gus Wiseman, Jun 22 2024

Keywords

• nonn

Comments

Run-lengths of A333254.

The first term other than 1 at an odd positions is at a(101) = 2.

Also run-lengths (differing by 0) of run-lengths (differing by 0) of run-lengths (differing by 1) of composite numbers.

Examples

			The odd primes are:
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, ...
with first differences:
2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, ...
with run-lengths:
2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, ...
with run-lengths a(n).
		

Crossrefs

Run-lengths of run-lengths of A046933(n) = A001223(n) - 1.

Run-lengths of A333254.

A000040 lists the primes.

A001223 gives differences of consecutive primes.

A027833 gives antirun lengths of odd primes (partial sums A029707).

A065855 counts composite numbers up to n.

A071148 gives partial sums of odd primes.

A373820 gives run-lengths of antirun-lengths of odd primes.

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

For composite runs: A005381, A008864, A054265, A176246, A251092, A373403.

Cf. A006560, A037201, A038664, A069010, A373824, A373825.

Programs

Mathematica

Length/@Split[Length /@ Split[Differences[Select[Range[3,1000],PrimeQ]]]//Most]//Most