A373406 Sum of the n-th maximal run of odd primes differing by two.

15, 24, 36, 23, 60, 37, 84, 47, 53, 120, 67, 144, 79, 83, 89, 97, 204, 216, 113, 127, 131, 276, 300, 157, 163, 167, 173, 360, 384, 396, 211, 223, 456, 233, 480, 251, 257, 263, 540, 277, 564, 293, 307, 624, 317, 331, 337, 696, 353, 359, 367, 373, 379, 383

Offset: 1

Author

Gus Wiseman, Jun 05 2024

Keywords

• nonn

Comments

The length of this run is given by A251092.

For this sequence we define a run to be an interval of positions at which consecutive terms differ by two. Normally, a run has consecutive terms differing by one, but odd prime numbers already differ by at least two.

Contains A054735 (sums of twin prime pairs) without its first two terms and A007510 (non-twin primes) as subsequences. - R. J. Mathar, Jun 07 2024

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
		

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: A025584, A054265, A067774, A251092 (or A175632), A373405, A373413, A373414.

A000040 lists the primes, differences A001223.

A046933 counts composite numbers between primes.

A065855 counts composite numbers up to n.

Cf. A005117, A007053, A029707, A038664, A293697, A350842, A371201.

Programs

Mathematica

Total/@Split[Select[Range[3,100],PrimeQ],#1+2==#2&]//Most