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

1,1

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.

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

Formula

a(2n) = 1.

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

Example

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

Mathematica

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

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.

Sequence in context: A374146 A277109 A359262 * A063062 A066056 A153284

Adjacent sequences: A373400 A373401 A373402 * A373404 A373405 A373406

Keyword

nonn

Author

Gus Wiseman, Jun 05 2024

Status

approved