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

1,1

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.

Links

Table of n, a(n) for n=1..47.

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

Example

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

Mathematica

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

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.

Sequence in context: A358342 A039584 A191717 * A136131 A143546 A069066

Adjacent sequences: A373402 A373403 A373404 * A373406 A373407 A373408

Keyword

nonn

Author

Gus Wiseman, Jun 05 2024

Status

approved