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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS 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 x-axis). 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] // Flatten (* Jean-François 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

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Last modified March 31 20:29 EDT 2023. Contains 361672 sequences. (Running on oeis4.)