|
|
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.
|
|
2
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
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
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|