A309701 Primes with record Manhattan distance from origin. When starting rightwards in a grid, turn left after a prime number. If not, walk straight on.

2, 3, 11, 29, 59, 97, 151, 193, 211, 223, 239, 281, 307, 311, 331, 337, 479, 541, 593, 613, 631, 641, 659, 877, 881, 907, 911, 997, 1409, 1861, 1907, 2267, 2281, 2287, 2309, 2311, 2503, 2579, 2609, 2617, 2657, 2671, 2677, 3671, 3691, 3697, 3727, 3761, 3767, 3793, 3797, 4201, 4327, 4357, 4391, 4397, 4507, 4721, 4751, 4909

Offset

1,1

Comments

This sequence differs from A309755 where the Euclidean distance is used.

Links

Pieter Post, Table of n, a(n) for n = 1..166

Example

Grid of the first 34 steps. 0 represents (0,0).
xx  xx   xx   31   30    29
xx  xx   xx   32   xx    28
xx  xx   xx   33   xx    27
xx  xx   xx   34   xx    26
xx 5/17 4/16 3/15  14   13/25
x 0/6/18  1    2   xx   12/24
xx 7/19 8/20 9/21 10/22 11/23
2 (2,0) is 2 steps away from the origin, 3 (2,1) has a distance of 3. Next record distance is 11 (4,-1), distance 5. Next is 29 (4,5), distance 9.

Mathematica

step[n_] := Switch[n, 0, {1, 0}, 1, {0, 1}, 2, {-1, 0}, 3, {0, -1}]; r = {0, 0}; q = 0; s={}; rm=0; Do[p = NextPrime[q]; r += step[Mod[n, 4]] * (p-q); r1 = Total @ Abs @ r; If[r1 > rm, rm = r1; AppendTo[s, p]]; q = p, {n, 0, 3000}]; s (* Amiram Eldar, Aug 15 2019 *)

Prog

(Python)
def prime(z):
    isPrime=True
    for y in range(2, int(z**0.5)+1) :
        if z%y==0:
            isPrime=False
            break
    return isPrime
m, n, g, h=[], [], [1, 0, -1, 0], [0, 1, 0, -1]
for c in range (2, 10000):
    if prime(c)==True:
        m.append(c)
ca, cb, cc=2, 0, 0
for j in range(2, 10000):
    if j in m:
        cc=cc+1
        cd, ce=g[cc%4], h[cc%4]
    ca, cb=ca+cd, cb+ce
    n.append([j+1, ca, cb, abs(ca)+abs(cb)])
v=2
for j in n:
    if j[3]>v and j[0] in m:
        print (j)
        v=j[3]
(PARI) upto(n) = {my(pos = [0, 0], rotateLeft = [0, -1; 1, 0], step = [1, 0], recordDistance = 0, q = 0, res = List(), i = 0); forprime(p = 2, n, pos += (p - q) * step; step *= rotateLeft; if(abs(pos[1]) + abs(pos[2]) > recordDistance, i++; recordDistance = abs(pos[1]) + abs(pos[2]); listput(res, p)); q = p); res} \\ David A. Corneth, Aug 15 2019

Crossrefs

Cf. A000040, A309755.

Sequence in context: A181956 A237038 A309755 * A243896 A202211 A104081

Adjacent sequences: A309698 A309699 A309700 * A309702 A309703 A309704

Keyword

nonn

Author

Pieter Post, Aug 13 2019

Status

approved