A162802 -id:A162802 - cp's OEIS frontend

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

Omar E. Pol, Jul 04 2009

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

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

Nathaniel Johnston, Table of n, a(n) for n = 1..10000
Omar E. Pol, Graph of the mountain path function for prime numbers

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

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

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

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

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

Edited by Omar E. Pol, Jul 16 2009

A162800 a(n) = n-th grid point that is covered by the zig-zag function for prime numbers such that the grid point is a vertex in the graph of the function.

Original entry on oeis.org

0, 2, 4, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, 42, 45, 50, 56, 60, 64, 69, 72, 76, 81, 86, 93, 99, 102, 105, 108, 111, 120, 129, 134, 138, 144, 150, 154, 160, 165, 170, 176, 180, 186, 192, 195, 198, 205, 217, 225, 228, 231, 236, 240, 246, 254, 260, 266, 270, 274, 279

Offset: 0

Omar E. Pol, Jul 16 2009

Also {0, 2} together the numbers A024675.

See A162345 for the first differences.

Paolo Xausa, Table of n, a(n) for n = 0..10000

Cf. A000040, A006005, A024675, A058296, A079424, A162345, A162801, A162802.

Join[{0, 2}, Most[#] + Differences[#]/2] & [Prime[Range[2, 100]]] (* Paolo Xausa, Jun 17 2024 *)

Edited by Omar E. Pol, Jul 18 2009

A162801 Bisection of A162800.

Original entry on oeis.org

0, 4, 9, 15, 21, 30, 39, 45, 56, 64, 72, 81, 93, 102, 108, 120, 134, 144, 154, 165, 176, 186, 195, 205, 225, 231, 240, 254, 266, 274, 282, 300, 312, 324, 342, 351, 363, 376, 386, 399, 414, 426, 436, 446, 459, 465, 483, 495, 506, 522, 544, 560, 570, 582, 596

Offset: 1

Omar E. Pol, Jul 16 2009

Essentially the same as A058296.

Cf. A058296, A079424, A162345, A162802.

cp's OEIS Frontend

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

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A162800 a(n) = n-th grid point that is covered by the zig-zag function for prime numbers such that the grid point is a vertex in the graph of the function.

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A162801 Bisection of A162800.

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