A373403 Length of the n-th maximal antirun of composite numbers differing by more than one.

3, 1, 3, 1, 3, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 1, 3, 1, 1, 1, 2, 1, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 3, 1, 3, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1

Offset: 1

Author

Gus Wiseman, Jun 05 2024

Keywords

• nonn

Comments

This antirun ranges from A005381 (with 4 prepended) to A068780, with sum A373404.

An antirun of a sequence (in this case A002808) is an interval of positions such that consecutive terms differ by more than one.

Examples

			Row-lengths of:
   4   6   8
   9
  10  12  14
  15
  16  18  20
  21
  22  24
  25
  26
  27
  28  30  32
  33
  34
  35
  36  38
  39
  40  42  44
		

Links

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

Crossrefs

Functional neighbors: A005381, A027833 (partial sums A029707), A068780, A176246 (rest of A046933, firsts A073051), A373127, A373404, A373409.

A000040 lists the primes, differences A001223.

A046933 counts composite numbers between primes.

A065855 counts composite numbers up to n.

Cf. A005117, A038664, A053767, A067970, A174965, A196274, A373400, A373573.

Programs

Mathematica

Length/@Split[Select[Range[100],CompositeQ],#1+1!=#2&]//Most

Formula

a(2n) = 1.

a(2n - 1) = A196274(n) for n > 1.