A373404 Sum of the n-th maximal antirun of composite numbers differing by more than one.

18, 9, 36, 15, 54, 21, 46, 25, 26, 27, 90, 33, 34, 35, 74, 39, 126, 45, 94, 49, 50, 51, 106, 55, 56, 57, 180, 63, 64, 65, 134, 69, 216, 75, 76, 77, 158, 81, 166, 85, 86, 87, 178, 91, 92, 93, 94, 95, 194, 99, 306, 105, 324, 111, 226, 115, 116, 117, 118, 119

Offset: 1

Author

Gus Wiseman, Jun 05 2024

Keywords

• nonn

Comments

The length of this antirun is given by A373403.

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

Examples

			Row sums 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

Partial sums are a subset of A053767 (partial sums of composite numbers).

Functional neighbors: A005381, A054265, A068780, A373403, A373405, A373411, A373412.

A000040 lists the primes, differences A001223.

A002808 lists the composite numbers, differences A073783.

A046933 counts composite numbers between primes.

A065855 counts composite numbers up to n.

Cf. A003114, A027833, A038664, A293697, A350842 (strict A350844), A371201.

Programs

Mathematica

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