The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A188552 Prime numbers at locations of angle turns in pentagonal spiral. 1
2, 3, 5, 7, 11, 17, 23, 31, 59, 71, 83, 97, 127, 179, 199, 241, 263, 311, 337, 419, 449, 479, 577, 647, 683, 839, 881, 967, 1103, 1151, 1249, 1511, 1567, 2111, 2243, 2311, 2591, 2663, 2887, 2963, 3041, 3119, 3361, 3527, 3697, 4049, 4139, 4231, 4703, 4801, 4999, 5099 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
2, 5, and primes in A056220 (lower vertical in pdf) and primes in A142463 (upper vertical). [Joerg Arndt, Apr 13 2011]
The link gives an illustration with three figures: Figure 1 contains the prime numbers at locations of angle turns in a pentagonal spiral; Figure 2 contains the prime numbers in a pentagonal spiral; Figure 3 shows a variety of sequences that are associated with the numbers of the lines and diagonals in the pentagonal spiral. For example, the sequence A033537 given by the formula n(2n+5) generates the sequence {0, 7, 18, 33, 52, 75, ... } and the corresponding line in the spiral is { 7, 18, 33, 52, 75, ... }.
LINKS
EXAMPLE
The pentagonal spiral's changes of direction (vertices) occur at the primes 2, 3, 5, 7, 11, 17, 23 ...
MAPLE
with(numtheory): T:=array(1..300):k:=1:for n from 1 to 50 do:x1:= 2*n^2 -1:
T[k]:=x1: x2:= (n+1)*(2*n-1): T[k+1]:=x2:x3:=2*n^2+2*n-1 : T[k+2]:=x3:x4:= 2*n*(n+1):
T[k+3]:=x4:x5:=n*(2*n+3): T[k+4]:=x5:k:=k+5:od: for p from 1 to 250 do:z:= T[p]:if
type(z, prime)= true then printf(`%d, `, z):else fi:od:
CROSSREFS
Cf. A188551.
Sequence in context: A005105 A086566 A235213 * A104892 A065436 A068523
KEYWORD
nonn
AUTHOR
Michel Lagneau, Apr 04 2011
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 21 16:41 EDT 2024. Contains 372738 sequences. (Running on oeis4.)