A160792 Vertex number of a rectangular spiral related to prime numbers. The distances between nearest edges of the spiral that are parallel to the initial edge are the prime numbers, while the distances between nearest edges perpendicular to the initial edge are all one.

0, 1, 3, 5, 10, 13, 23, 27, 44, 49, 77, 83, 124, 131, 189, 197, 274, 283, 383, 393, 522, 533, 693, 705, 902, 915, 1153, 1167, 1448, 1463, 1791, 1807, 2188, 2205, 2645, 2663, 3164, 3183, 3751, 3771, 4410, 4431, 5143, 5165, 5956, 5979, 6853, 6877, 7840, 7865

Offset: 0

Author

Omar E. Pol, May 29 2009

Keywords

• easy
• nonn

Comments

First differences give A160793. - Omar E. Pol, Oct 31 2011

Links

• Nathaniel Johnston, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A000040, A160790, A160791, A160793.

Programs

Maple

A160792 := proc(n) option remember: if(n<=1)then return n: fi: if(n mod 2 = 0)then return procname(n-1)+add(ithprime(j),j=1..n/2): fi: return procname(n-1)+ceil(n/2): end: seq(A160792(n),n=0..49); # Nathaniel Johnston, Jun 16 2011

Formula

a(2n) = a(2n-1) + Sum_{j=1..n} prime(j); a(2n+1) = a(2n) + n + 1 for n >= 1. - Nathaniel Johnston, Jun 16 2011

Extensions

Terms after a(10) and edited by Nathaniel Johnston, Jun 16 2011