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

0,3

Comments

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

Links

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

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

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

Crossrefs

Cf. A000040, A160790, A160791, A160793.

Sequence in context: A031878 A345890 A265282 * A308759 A137395 A001767

Adjacent sequences: A160789 A160790 A160791 * A160793 A160794 A160795

Keyword

easy,nonn

Author

Omar E. Pol, May 29 2009

Extensions

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

Status

approved