A373820 - OEIS

A373820

Run-lengths (differing by 0) of antirun-lengths (differing by > 2) of odd primes.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Run-lengths of the version of A027833 with 1 prepended.

LINKS

Table of n, a(n) for n=1..87.

Gus Wiseman, Four statistics for runs and antiruns of prime, nonprime, squarefree, and nonsquarefree numbers.

EXAMPLE

The antiruns of odd primes (differing by > 2) begin:

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

2 2

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 prime runs: A001359, A006512, A025584, A067774, A373405, A373406.

For composite runs: A005381, A054265, A068780, A373403, A373404.

Cf. A005117, A006560, A006562, A037201, A038664, A049579, A073051, A076259, A122535, A176246.

Sequence in context: A030599 A237413 A157343 * A102679 A025146 A067397

Adjacent sequences: A373817 A373818 A373819 * A373821 A373822 A373823

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 22 2024

STATUS

approved