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A188552 Prime numbers at locations of angle turns in pentagonal spiral. 1

%I #19 Oct 04 2017 02:11:57

%S 2,3,5,7,11,17,23,31,59,71,83,97,127,179,199,241,263,311,337,419,449,

%T 479,577,647,683,839,881,967,1103,1151,1249,1511,1567,2111,2243,2311,

%U 2591,2663,2887,2963,3041,3119,3361,3527,3697,4049,4139,4231,4703,4801,4999,5099

%N Prime numbers at locations of angle turns in pentagonal spiral.

%C 2, 5, and primes in A056220 (lower vertical in pdf) and primes in A142463 (upper vertical). [_Joerg Arndt_, Apr 13 2011]

%C 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, ... }.

%H Michel Lagneau, <a href="/A188552/a188552_4.pdf">Illustration of the numbers in the pentagonal spiral</a>

%e The pentagonal spiral's changes of direction (vertices) occur at the primes 2, 3, 5, 7, 11, 17, 23 ...

%p with(numtheory): T:=array(1..300):k:=1:for n from 1 to 50 do:x1:= 2*n^2 -1:

%p 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):

%p 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

%p type(z,prime)= true then printf(`%d, `,z):else fi:od:

%Y Cf. A188551.

%K nonn

%O 1,1

%A _Michel Lagneau_, Apr 04 2011

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)