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A373819
Run-lengths (differing by 0) of the run-lengths (differing by 2) of the odd primes.
5
1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 4, 2, 3, 2, 4, 3, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 3, 1, 10, 2, 4, 1, 7, 1, 4, 1, 3, 1, 2, 1, 1, 1, 2, 1, 18, 3, 2, 1, 2, 1, 17, 2, 1, 2, 2, 1, 6, 1, 9, 1, 3, 1, 1, 1, 1, 1, 1, 1, 8, 1, 3, 1, 2, 2, 15, 1, 1, 1, 4, 1, 1, 1, 1, 1, 7, 1
OFFSET
1,2
COMMENTS
Run-lengths of A251092.
EXAMPLE
The odd primes begin:
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
59 61
67
71 73
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, 1, ...
which have runs beginning:
3
2 2
1
2
1
2
1 1
2
1
2
1 1 1 1
2 2
1 1 1
with lengths a(n).
MATHEMATICA
Length/@Split[Length/@Split[Select[Range[3, 1000], PrimeQ], #1+2==#2&]//Most]//Most
CROSSREFS
Run-lengths of A251092.
For antiruns we have A373820, run-lengths of A027833 (if we prepend 1).
Positions of first appearances are A373825, sorted A373824.
A000040 lists the primes.
A001223 gives differences of consecutive primes, run-lengths A333254, run-lengths of run-lengths A373821.
A046933 counts composite numbers between primes.
A065855 counts composite numbers up to n.
A071148 gives partial sums of odd primes.
For composite runs: A005381, A054265, A068780, A373403, A373404.
Sequence in context: A277231 A122934 A072170 * A368885 A294932 A327804
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 20 2024
STATUS
approved