A373819 Run-lengths (differing by 0) of the run-lengths (differing by 2) of the odd primes.

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

Author

Gus Wiseman, Jun 20 2024

Keywords

• nonn

Comments

Run-lengths of A251092.

Examples

			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).
		

Links

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

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

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

Cf. A005117, A006560, A006562, A029707, A037201, A038664, A076259, A176246.

Programs

Mathematica

Length/@Split[Length/@Split[Select[Range[3,1000], PrimeQ],#1+2==#2&]//Most]//Most