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 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 Michel Lagneau, Illustration of the numbers in the pentagonal spiral 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 Adjacent sequences:  A188549 A188550 A188551 * A188553 A188554 A188555 KEYWORD nonn AUTHOR Michel Lagneau, Apr 04 2011 STATUS approved

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Last modified January 24 19:03 EST 2022. Contains 350565 sequences. (Running on oeis4.)