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A295085 Numbers k such that {k*phi} < 0.25 or {k*phi} > 0.75, where phi is the golden ratio (1 + sqrt(5))/2 and { } denotes fractional part. 0
2, 3, 5, 8, 10, 11, 13, 16, 18, 21, 23, 24, 26, 29, 31, 32, 34, 36, 37, 39, 42, 44, 45, 47, 50, 52, 53, 55, 57, 58, 60, 63, 65, 66, 68, 71, 73, 76, 78, 79, 81, 84, 86, 87, 89, 91, 92, 94, 97, 99, 100, 102, 105, 107, 110, 112, 113, 115, 118, 120, 121, 123, 126, 128, 131, 133, 134, 136, 139, 141, 142, 144, 146 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Numbers k such that k rotations by the golden angle yields a result between -Pi/2 and Pi/2 radians.

LINKS

Table of n, a(n) for n=0..72.

P. Prusinkiewicz and A. Lindenmayer, Chapter 4, Phyllotaxis, The Algorithmic Beauty of Plants (1990).

MATHEMATICA

Select[Range@ 150, Or[# < 1/4, # > 3/4] &@ FractionalPart[# GoldenRatio] &] (* Michael De Vlieger, Nov 15 2017 *)

PROG

(R) Phi=(sqrt(5)+1)/2 # Golden ratio

fp=function(x) x-floor(x) # fractional part

M=200

alpha=fp((1:M)*Phi) # angles in turn

PF=c(); PB=c() # Phyllotaxis front and back

for (i in 1:M) if ((alpha[i]>0.25)*(alpha[i]<0.75)) PB=c(PB, i) else PF=c(PF, i)

(PARI) isok(n) = my(phi=(1+sqrt(5))/2); (frac(n*phi)<1/4) || (frac(n*phi)>3/4); \\ Michel Marcus, Nov 14 2017

CROSSREFS

Complement of A190250 (as has been proved), thus, intertwining of A190249 and A190251.

Cf. A001622.

Sequence in context: A028840 A189143 A047605 * A153000 A222172 A326379

Adjacent sequences:  A295082 A295083 A295084 * A295086 A295087 A295088

KEYWORD

nonn,easy

AUTHOR

Burghard Herrmann, Nov 14 2017

STATUS

approved

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Last modified January 18 13:49 EST 2020. Contains 331010 sequences. (Running on oeis4.)