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

1,10

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, Table of n, a(n) for n = 1..10000

Karl-Heinz Hofmann, Graphic example.

Karl-Heinz Hofmann, Graphic together with the first 10000 primes.

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)

Crossrefs

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

Cf. A054569, A033951, A016754, A357745.

Sequence in context: A113716 A220652 A169654 * A088158 A136449 A209427

Adjacent sequences: A357741 A357742 A357743 * A357745 A357746 A357747

Keyword

nonn

Author

Karl-Heinz Hofmann, Dec 01 2022

Status

approved