A162200 Number on the positive y axis of the n-th horizontal component in the graph of the "mountain path" function for prime numbers.

0, 0, 2, 2, 5, 4, 7, 6, 9, 6, 10, 8, 13, 12, 15, 12, 18, 16, 20, 17, 20, 18, 23, 20, 27, 23, 26, 25, 28, 27, 36, 29, 34, 32, 38, 34, 38, 34, 39, 36, 42, 40, 46, 42, 45, 44, 51, 41, 49, 48, 51, 48, 52, 48, 56, 52, 58, 56, 60, 57, 60, 56, 68, 61, 64, 63, 72, 64, 72, 68, 71, 68, 75

Offset: 1

Author

Omar E. Pol, Jun 28 2009

Keywords

• easy
• nonn

Comments

Note that the n-th horizontal component is an edge with length equal to 1 (see the link: Graph of the mountain path function).

See A162201 for the first differences.

Links

• Omar E. Pol, Graph of the mountain path function for prime numbers
• Omar E. Pol, Illustration: The mountain path of the primes

Crossrefs

Cf. A000040, A006005, A008578, A162201, A162202, A162203, A162340, A162341, A162342, A162343, A162344.

Programs

Maple

A031131 := proc(n) ithprime(n+2)-ithprime(n) ; end: A052288 := proc(n) A031131(n)/2 ; end: A162201 := proc(n) if n <= 2 then 2*(n-1); elif n mod 2 = 0 then A052288(n-1) ; else 2-A052288(n-1) ; fi; end: A162200 := proc(n) add(A162201(j),j=1..n-1) ; end: seq(A162200(n),n=1..150) ; # R. J. Mathar, Jul 15 2009

Extensions

Edited by Omar E. Pol, Jul 02 2009

More terms from R. J. Mathar, Jul 15 2009