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

1,1

Comments

Run-sums of A251092.

Links

Table of n, a(n) for n=1..86.

Example

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).

Mathematica

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

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.

Sequence in context: A226063 A326748 A204999 * A294731 A085710 A248004

Adjacent sequences: A373825 A373826 A373827 * A373829 A373830 A373831

Keyword

nonn,new

Author

Gus Wiseman, Jun 23 2024

Status

approved