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A373820
Run-lengths (differing by 0) of antirun-lengths (differing by > 2) of odd primes.
10
2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1
OFFSET
1,1
COMMENTS
Run-lengths of the version of A027833 with 1 prepended.
EXAMPLE
The antiruns of odd primes (differing by > 2) begin:
3
5
7 11
13 17
19 23 29
31 37 41
43 47 53 59
61 67 71
73 79 83 89 97 101
103 107
109 113 127 131 137
139 149
151 157 163 167 173 179
181 191
193 197
199 211 223 227
229 233 239
241 251 257 263 269
271 277 281
with lengths:
1, 1, 2, 2, 3, 3, 4, 3, 6, 2, 5, 2, 6, 2, 2, ...
with runs:
1 1
2 2
3 3
4
3
6
2
5
2
6
2 2
4
3
5
3
4
with lengths a(n).
MATHEMATICA
Length/@Split[Length/@Split[Select[Range[3, 1000], PrimeQ], #2-#1>2&]//Most]//Most
CROSSREFS
Run-lengths of A027833 (if we prepend 1), partial sums A029707.
For runs we have A373819, run-lengths of A251092.
Positions of first appearances are A373827, sorted A373826.
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: A030599 A237413 A157343 * A102679 A025146 A067397
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 22 2024
STATUS
approved