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URL: https://oeis.org/A357744

⇱ A357744 - OEIS

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A357744
a(n) is the least k such that prime(n) * k occurs in one of the eight main spokes of a square spiral with 1 in the center.
1
1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 25, 1, 17, 1, 59, 1, 13, 37, 1, 4, 3, 13, 5, 1, 21, 8, 2, 4, 1, 131, 3, 1, 2, 1, 1, 1, 2, 37, 4, 13, 58, 7, 1, 34, 1, 7, 23, 4, 1, 29, 1, 251, 1, 5, 25, 3, 13, 1, 7, 30, 1, 311, 31, 38, 3, 49, 3, 6, 5, 37, 19, 16, 7, 5, 149, 3, 1, 7, 419, 1, 1, 91, 10, 2
OFFSET
1,10
COMMENTS
Numbers on the spokes of the spiral are A357745.
a(n) = 1 when prime(n) is directly on a main spoke.
a(n) <= prime(n) since odd squares are on the southeast spoke (A016754).
LINKS
Karl-Heinz Hofmann, Graphic example.
PROG
(Python)
from sympy import sieve
A357744, A357745, aupto = [], [], 82
for n in range (1, sieve[aupto]**2):
A357745.append(((n+3)**2 >> 4) + 1 if n % 8 != 1 else (n+3)**2 >> 4)
for p in sieve[1:aupto + 1]:
k = 1
while (p*k) not in A357745: k += 1
A357744.append(k)
print(A357744)
KEYWORD
nonn
AUTHOR
Karl-Heinz Hofmann, Dec 01 2022
STATUS
approved