A373822 Sum of the n-th maximal run of first differences of odd primes.

4, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 12, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, 14, 4, 6, 2, 10, 2, 12, 4, 12, 2, 10, 2, 4, 2, 24, 4, 2, 4, 6, 2, 10, 18, 2, 6, 4, 2, 10, 14, 4, 2, 4, 14, 6, 10, 2, 4, 6, 8, 12, 4, 6, 8, 4, 8, 10, 2, 10, 2, 6, 4, 6, 8, 4, 2, 4

Offset

1,1

Comments

Run-sums of A001223. For run-lengths instead of run-sums we have A333254.

Links

Table of n, a(n) for n=1..81.

Example

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 sums a(n).

Mathematica

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

Crossrefs

Run-sums of A001223.

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

Dividing by two gives A373823.

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.

Sequence in context: A260486 A193514 A112108 * A021230 A273278 A213089

Adjacent sequences: A373819 A373820 A373821 * A373823 A373824 A373825

Keyword

nonn

Author

Gus Wiseman, Jun 22 2024

Status

approved