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A309755
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Primes with record Euclidean distance from the origin. When starting rightwards in a grid, turn left after a prime number, if not walk straight on.
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3
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2, 3, 11, 29, 59, 97, 149, 151, 191, 193, 211, 223, 239, 263, 281, 307, 311, 331, 337, 593, 613, 631, 641, 653, 659, 853, 857, 877, 881, 907, 911, 967, 971, 991, 997, 1801, 1811, 1847, 1861, 1901, 1907, 2251, 2267, 2281, 2287, 2309, 2311, 2657, 2671, 2677, 3163, 3167, 3187, 3191, 3299, 3319, 3343, 3691, 3697, 3719, 3727
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OFFSET
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1,1
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COMMENTS
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Cells can contain more than one number.
This sequence differs from A309701, where the Manhattan distance is taken.
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LINKS
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EXAMPLE
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Grid of the first 34 steps. 0 (second cell in sixth row) 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
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2 (2,0) is two steps away from the origin, 3 (2,1) is at a distance of sqrt(5). Next record distance is 11 (4,-1), at distance sqrt(17). Next is 29 (4,5), at distance sqrt(41).
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MATHEMATICA
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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 @ (r^2); If[r1 > rm, rm = r1; AppendTo[s, p]]; q = p, {n, 0, 3000}]; s (* Amiram Eldar, Aug 15 2019 *)
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PROG
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(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]
z=10000
for c in range (2, z):
if prime(c)==True:
m.append(c)
ca, cb, cc=2, 0, 0
for j in range(2, z):
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, ((ca)**2+(cb)**2)**(0.5)])
#print (j+1, ca, cb)
v=2
for j in n:
if j[3]>v and j[0] in m:
print (j)
v=j[3]
(PARI) z=0; d=1; m=0; for (n=1, 3727, z+=d; if (isprime(n), d*=I; if (m<norm(z), m=norm(z); print1 (n ", ")))) \\ Rémy Sigrist, Aug 15 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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