A373405 Sum of the n-th maximal antirun of odd primes differing by more than two.

3, 5, 18, 30, 71, 109, 202, 199, 522, 210, 617, 288, 990, 372, 390, 860, 701, 1281, 829, 1194, 1645, 4578, 852, 2682, 4419, 3300, 2927, 2438, 1891, 2602, 14660, 1632, 1650, 3378, 3480, 18141, 2052, 3121, 2112, 4310, 8922, 13131, 6253, 3851, 3889, 3929, 13788

Offset: 1

Author

Gus Wiseman, Jun 05 2024

Keywords

• nonn

Comments

The length of this run is given by A027833 (except initial term).

An antirun of a sequence (in this case A000040\{2}) is an interval of positions at which consecutive terms differ by more than one.

Examples

			Row-sums of:
   3
   5
   7  11
  13  17
  19  23  29
  31  37  41
  43  47  53  59
  61  67  71
  73  79  83  89  97 101
		

Links

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

Crossrefs

The partial sums are a subset of A071148 (partial sums of odd primes).

Functional neighbors: A001359, A006512, A027833 (partial sums A029707), A373404, A373406, A373411, A373412.

A000040 lists the primes, differences A001223.

A002808 lists the composite numbers, differences A073783.

Cf. A025157, A038664, A046933, A293697, A350842 (strict A350844), A371201.

Programs

Mathematica

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