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

Author

Omar E. Pol, Jun 28 2009

Keywords

• easy
• sign

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

• 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, A162200, 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: 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

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)

Extensions

Edited by Omar E. Pol, Jul 02 2009

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