

A162345


Length of nth edge in the graph of the zigzag function for prime numbers.


8



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
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OFFSET

1,1


COMMENTS

Also, first differences of A162800.
Also {2, 2, } together with the numbers A052288.
Note that the graph of the zigzag 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(n1))/2. Similarly, because half the numbers between prime(n1) and prime(n+1) are closer to prime(n) than any other prime, A115061(n) = (prime(n+1)  prime(n1))/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(n1))/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(n1))/2: end: seq(A162345(n), n=1..100); # Nathaniel Johnston, Jun 25 2011


MATHEMATICA

Join[{2, 2}, Table[(Prime[n+1]  Prime[n1])/2, {n, 3, 100}]] (* Vincenzo Librandi, Dec 19 2016 *)


PROG

(MAGMA) [2, 2] cat[(NthPrime(n+1)NthPrime(n1))/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



