A373828 Run-sums (differing by 0) of run-lengths (differing by 2) of odd primes.

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

Offset: 1

Author

Gus Wiseman, Jun 23 2024

Keywords

• nonn

Comments

Run-sums of A251092.

Examples

			The odd primes are:
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, ...
with runs:
{3,5,7}, {11,13}, {17,19}, {23}, {29,31}, {37}, {41,43}, {47}, {53}, ...
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, ...
with runs:
{3}, {2,2}, {1}, {2}, {1}, {2}, {1,1}, {2}, {1}, {2}, {1,1,1,1}, {2,2}, ...
with sums a(n).
		

Crossrefs

Run-sums of A251092.

The run-lengths (instead of run-sums) are A373819, firsts A373825, A373824.

A000040 lists the primes.

A001223 gives first differences of primes.

A027833 gives antirun-lengths of primes > 3 (prepended run-lengths A373820).

A046933 counts composite numbers between primes.

A071148 gives partial sums of odd primes.

A333254 gives run-lengths of first differences of primes.

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

Cf. A006560, A006562, A029707, A054265, A067774, A373403, A373404, A373406.

Programs

Mathematica

Total/@Split[Length /@ Split[Select[Range[3,10000],PrimeQ], #1+2==#2&]//Most]//Most