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A373828
Run-sums (differing by 0) of run-lengths (differing by 2) of odd primes.
0
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.
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.
Sequence in context: A226063 A326748 A204999 * A294731 A085710 A248004
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 23 2024
STATUS
approved