

A297347


List of ycoordinates in the Babylonian Spiral.


3



0, 1, 2, 2, 1, 1, 4, 7, 10, 10, 9, 6, 2, 3, 8, 13, 17, 20, 20, 19, 17, 13, 7, 0, 7, 13, 15, 12, 7, 1, 9, 17, 23, 26, 21, 13, 4, 5, 14, 22, 25, 21, 14, 6, 4, 14, 23, 26, 19, 9, 0, 0, 1, 3, 11, 20, 30, 41, 53, 65, 76, 78, 71, 59, 48, 44, 53, 63, 75, 88, 101
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OFFSET

1,3


COMMENTS

The "Babylonian Spiral" is defined and illustrated in A256111.


LINKS

Alex Meiburg, Table of n, a(n) for n = 1..10000
Lars Blomberg, Illustrations of 100, 1000 and 10000 terms of the spiral.
MathPickle, Babylonian Spiral


EXAMPLE

The first few points are (0,0), (0,1), (1,2), (3,2)  thus the sequence starts out 0, 1, 2, 2.


MATHEMATICA

NextVec[{x_, y_}] :=
Block[{n = x^2 + y^2 + 1}, While[SquaresR[2, n] == 0, n++];
TakeSmallestBy[
Union[Flatten[(Transpose[
Transpose[Tuples[{1, 1}, 2]] #] & /@
({{#[[1]], #[[2]]}, {#[[2]], #[[1]]}})) & /@
PowersRepresentations[n, 2, 2], 2]],
Mod[ArcTan[#[[2]], #[[1]]]  ArcTan[y, x], 2 Pi] &, 1][[1]]
]
Accumulate[NestList[NextVec, {0, 1}, 500]][[;; , 2]]


CROSSREFS

The xcoordinates are given in A297346. Norms of vectors are given in A256111.
Sequence in context: A132311 A254414 A199802 * A121697 A225201 A124976
Adjacent sequences: A297344 A297345 A297346 * A297348 A297349 A297350


KEYWORD

easy,sign,look


AUTHOR

Alex Meiburg, Dec 28 2017


STATUS

approved



