A357745 -id:A357745 - cp's OEIS frontend

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, 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

Karl-Heinz Hofmann, Dec 01 2022

nonn

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).

Karl-Heinz Hofmann, Table of n, a(n) for n = 1..10000
Karl-Heinz Hofmann, Graphic example.
Karl-Heinz Hofmann, Graphic together with the first 10000 primes.

Cf. A000040, A054552, A054554, A054556, A053755, A054567.

Cf. A054569, A033951, A016754, A357745.

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)

cp's OEIS Frontend

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.

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