A373823 Half the sum of the n-th maximal run of first differences of odd primes.

2, 2, 1, 2, 1, 2, 3, 1, 3, 2, 1, 2, 6, 1, 3, 2, 1, 3, 2, 3, 4, 2, 1, 2, 1, 2, 7, 2, 3, 1, 5, 1, 6, 2, 6, 1, 5, 1, 2, 1, 12, 2, 1, 2, 3, 1, 5, 9, 1, 3, 2, 1, 5, 7, 2, 1, 2, 7, 3, 5, 1, 2, 3, 4, 6, 2, 3, 4, 2, 4, 5, 1, 5, 1, 3, 2, 3, 4, 2, 1, 2, 6, 4, 2, 4, 2, 3

Offset: 1

Author

Gus Wiseman, Jun 22 2024

Keywords

• nonn

Comments

Halved run-sums of A001223.

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 runs:
(2,2), (4), (2), (4), (2), (4), (6), (2), (6), (4), (2), (4), (6,6), ...
with halved sums a(n).
		

Crossrefs

Halved run-sums of A001223.

For run-lengths we have A333254, run-lengths of run-lengths A373821.

Multiplying by two gives A373822.

A000040 lists the primes.

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

A046933 counts composite numbers between primes.

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, A373405, A373406.

Cf. A037201, A038664, A054265, A176246, A251092, A373404, A373825.

Programs

Mathematica

Total/@Split[Differences[Select[Range[3,1000],PrimeQ]]]/2