

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
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OFFSET

1,1


COMMENTS

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*n1): T[k+1]:=x2:x3:=2*n^2+2*n1 : 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



KEYWORD

nonn


AUTHOR



STATUS

approved



