A162201 First differences of A162200.

0, 2, 0, 3, -1, 3, -1, 3, -3, 4, -2, 5, -1, 3, -3, 6, -2, 4, -3, 3, -2, 5, -3, 7, -4, 3, -1, 3, -1, 9, -7, 5, -2, 6, -4, 4, -4, 5, -3, 6, -2, 6, -4, 3, -1, 7, -10, 8, -1, 3, -3, 4, -4, 8, -4, 6, -2, 4, -3, 3, -4, 12, -7, 3, -1, 9, -8, 8, -4, 3, -3, 7, -5, 6, -3, 5, -5, 6, -4, 9, -4, 6, -4, 4, -3

Offset

1,2

Comments

The absolute value of a(n) is also the length of the n-th vertical edge in the graph of the "mountain path" function for prime numbers.

See A162200 for the length of the n-th horizontal component.

Links

Table of n, a(n) for n=1..85.

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

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

Formula

From R. J. Mathar, Jul 15 2009: (Start)

a(n) = A052288(n-1) if n >= 2, n even.

a(n) = 2 - A052288(n-1) if n >= 3, n odd. (End)

Maple

A031131 := proc(n) ithprime(n+2)-ithprime(n) ; end: A052288 := proc(n) A031131(n)/2 ; end: A160173 := 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: seq(A160173(n), n=1..150) ; # R. J. Mathar, Jul 15 2009

Crossrefs

Cf. A000040, A006005, A008578, A162200, A162202, A162203, A162340, A162341, A162342, A162343, A162344.

Sequence in context: A375111 A324115 A029239 * A271722 A029219 A339373

Adjacent sequences: A162198 A162199 A162200 * A162202 A162203 A162204

Keyword

easy,sign

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