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
Links
- Nathaniel Johnston, Table of n, a(n) for n = 0..1000
Programs
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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
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
Extensions
Terms after a(12) and edited by Nathaniel Johnston, Jun 16 2011