A160794 Vertex number of a rectangular spiral related to Fibonacci numbers and prime numbers. The distances between nearest edges of the spiral that are parallel to the initial edge are the Fibonacci numbers, while the distances between nearest edges perpendicular to the initial edge are the prime numbers.

0, 1, 2, 5, 7, 13, 17, 28, 35, 53, 65, 94, 114, 156, 189, 248, 302, 380, 468, 569, 712, 842, 1074, 1235, 1611, 1809, 2418, 2657, 3643, 3925, 5521, 5850, 8433, 8815, 12995, 13436, 20200, 20702, 31647, 32216, 49926, 50566, 79222, 79935, 126302, 127094, 202118

Offset

0,3

Links

Nathaniel Johnston, Table of n, a(n) for n = 0..1000

Formula

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

Maple

A160794 := proc(n) option remember: if(n<=1)then return n: fi: if(n mod 2 = 0)then return procname(n-1)+add(combinat[fibonacci](j), j=1..n/2): fi: return procname(n-1)+add(ithprime(j), j=1..floor(n/2))+1: end: seq(A160794(n), n=0..46); # Nathaniel Johnston, Jun 16 2011

Crossrefs

Cf. A000040, A000045, A160790, A160792.

Sequence in context: A222532 A144256 A082555 * A092059 A260388 A169586

Adjacent sequences: A160791 A160792 A160793 * A160795 A160796 A160797

Keyword

easy,nonn

Author

Omar E. Pol, May 29 2009

Extensions

Terms after a(12) and edited by Nathaniel Johnston, Jun 16 2011

Status

approved