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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 23 20:00 EDT 2024. Contains 373653 sequences. (Running on oeis4.)