A162345 Length of n-th edge in the graph of the zig-zag function for prime numbers.

2, 2, 2, 3, 3, 3, 3, 3, 5, 4, 4, 5, 3, 3, 5, 6, 4, 4, 5, 3, 4, 5, 5, 7, 6, 3, 3, 3, 3, 9, 9, 5, 4, 6, 6, 4, 6, 5, 5, 6, 4, 6, 6, 3, 3, 7, 12, 8, 3, 3, 5, 4, 6, 8, 6, 6, 4, 4, 5, 3, 6, 12, 9, 3, 3, 9, 10, 8, 6, 3, 5, 7, 7, 6, 5, 5, 7, 6, 6, 9, 6, 6, 6, 4, 5, 5

Offset

1,1

Comments

Also, first differences of A162800.

Also {2, 2, } together with the numbers A052288.

Note that the graph of the zig-zag function for prime numbers is similar to the graph of the mountain path function for prime numbers but with exactly a vertex between consecutive odd noncomposite numbers (A006005).

This is the same as A115061 if n>1 (and also essentially equal to A052288). Proof: Because this is the first differences of A162800, which is {0,2} together with A024675, this sequence (for n>=3) is given by a(n) = (prime(n+1) - prime(n-1))/2. Similarly, because half the numbers between prime(n-1) and prime(n+1) are closer to prime(n) than any other prime, A115061(n) = (prime(n+1) - prime(n-1))/2 for n>=3 as well. - Nathaniel Johnston, Jun 25 2011

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..10000

Omar E. Pol, Graph of the mountain path function for prime numbers

Formula

a(n) = (prime(n+1) - prime(n-1))/2 for n>=3. - Nathaniel Johnston, Jun 25 2011

Example

Array begins:
=====
x, y
=====
2, 2;
2, 3;
3, 3;
3, 3;
5, 4;

Maple

A162345 := proc(n) if(n<=2)then return 2: fi: return (ithprime(n+1) - ithprime(n-1))/2: end: seq(A162345(n), n=1..100); # Nathaniel Johnston, Jun 25 2011

Mathematica

Join[{2, 2}, Table[(Prime[n+1] - Prime[n-1])/2, {n, 3, 100}]] (* Vincenzo Librandi, Dec 19 2016 *)

Prog

(Magma) [2, 2] cat[(NthPrime(n+1)-NthPrime(n-1))/2: n in [3..80]]; // Vincenzo Librandi, Dec 19 2016

Crossrefs

Cf. A000040, A006005, A008578, A024675, A052288, A162203, A162800, A162801, A162802.

Sequence in context: A063272 A127240 A097561 * A048689 A069923 A095840

Adjacent sequences: A162342 A162343 A162344 * A162346 A162347 A162348

Keyword

easy,nonn

Author

Omar E. Pol, Jul 04 2009

Extensions

Edited by Omar E. Pol, Jul 16 2009

Status

approved