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

1,3

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

Table of n, a(n) for n=1..73.

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

Omar E. Pol, Illustration: The mountain path of the primes

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

Crossrefs

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

Sequence in context: A241306 A336073 A266792 * A290289 A000019 A318196

Adjacent sequences: A162197 A162198 A162199 * A162201 A162202 A162203

Keyword

easy,nonn

Author

Omar E. Pol, Jun 28 2009

Extensions

Edited by Omar E. Pol, Jul 02 2009

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

Status

approved