

A233399


A "turtle transform" of the primes p=A000040: coordinates (x,y)=(a(2n),a(2n+1)) of a walk on the complex plane, where at step n the cursor turns by arg(i^p(n)), then moves p(n) units ahead.


5



0, 0, 2, 0, 2, 3, 7, 3, 7, 10, 4, 10, 4, 23, 13, 23, 13, 42, 10, 42, 10, 71, 41, 71, 41, 108, 0, 108, 0, 151, 47, 151, 47, 204, 106, 204, 106, 265, 173, 265, 173, 194, 246, 194, 246, 115, 163, 115, 163, 26, 260, 26, 260, 127, 363, 127, 363, 20
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OFFSET

0,3


LINKS

Table of n, a(n) for n=0..57.
M. F. Hasler, Turtle(prime) walk after 25 steps.
M. F. Hasler, Turtle(prime) walk after 60 steps.
M. F. Hasler, Turtle(prime) walk after the 99th step, drawn in red.


EXAMPLE

The cursor starts for n=0 at the origin (a(0)=a(1)=0), facing East (= direction of the xaxis). At step 1, prime(1)=2 leads to a turn left by 2*90 degrees (now facing West), then a step of two units into the new direction, to x+iy = 2, thus a(2)=2, a(3)=0. Prime(2)=3 leads to a turn left by 3*90 degrees, now facing North, and a step of 3 units in that direction, to x+iy = 2+3i, therefore a(4)=2, a(5)=3.


MATHEMATICA

Turtle[v_] := Module[{p, L, d}, p=0; L={p}; d=1; For[i=1, i <= Length[v], i++, d *= I^v[[i]]; AppendTo[L, p += d*v[[i]] ] ]; L]; {Re[#], Im[#]}& /@ Turtle[Prime /@ Range[60]] // Flatten (* JeanFrançois Alcover, Dec 11 2013, translated from PARI *)


PROG

(PARI) Turtle(v, p=0, L=[p], d=1)=for(i=1, #v, d*=I^v[i]; L=concat(L, p+=d*v[i])); L
(PARI) a(nMax)=concat(apply(z>[real(z), imag(z)], Turtle(primes(nMax))))


CROSSREFS

Sequence in context: A361651 A222753 A274568 * A226432 A072514 A071547
Adjacent sequences: A233396 A233397 A233398 * A233400 A233401 A233402


KEYWORD

sign,walk


AUTHOR

M. F. Hasler, Dec 08 2013


STATUS

approved



