A394484 Chebyshev distance between prime(n) and prime(n+1) on Ulam spiral.

1, 2, 2, 3, 2, 4, 2, 2, 3, 2, 6, 4, 2, 4, 3, 4, 2, 4, 4, 2, 6, 3, 6, 6, 4, 2, 4, 2, 2, 9, 4, 4, 2, 6, 2, 6, 6, 4, 3, 6, 2, 8, 2, 4, 2, 12, 12, 3, 2, 4, 6, 2, 10, 6, 6, 6, 2, 4, 4, 2, 7, 14, 4, 2, 4, 8, 6, 6, 2, 4, 6, 5, 6, 6, 2, 6, 8, 4, 8, 10, 2, 10, 2, 6, 3

Offset

1,2

Links

Table of n, a(n) for n=1..85.

Example

For n = 2 we are concerned with 2nd prime and 3rd prime: 3 and 5. Chebyshev distance between 3 and 5 on Ulam spiral is 2.

Prog

(Python)
import math
from sympy import prime
def ulam_coords(n):
    if n == 1:
        return (0, 0)
    k = math.ceil((math.sqrt(n) - 1) / 2)
    t = 2 * k
    m = (t + 1) ** 2
    if n >= m - t:
        return (k - (m - n), -k)
    m -= t
    if n >= m - t:
        return (-k, -k + (m - n))
    m -= t
    if n >= m - t:
        return (-k + (m - n), k)
    m -= t
    return (k, k - (m - n))
def seq(num):
    sequence = []
    for n in range(1, num + 1):
        p1 = prime(n)
        p2 = prime(n + 1)
        x1, y1 = ulam_coords(p1)
        x2, y2 = ulam_coords(p2)
        dist = max(abs(x1 - x2), abs(y1 - y2))
        sequence.append(dist)
    return sequence
print(seq(50))

Crossrefs

Cf. A000040, A214664, A214665, A391618.

Sequence in context: A359302 A366147 A367170 * A369306 A038148 A366742

Adjacent sequences: A394481 A394482 A394483 * A394485 A394486 A394487

Keyword

nonn

Author

Aitzaz Imtiaz, Mar 22 2026

Status

approved