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A139401 If n is a square, a(n) is 0. Otherwise, a(n) is the smallest number k such that n is not a quadratic residue modulo k. 3
0, 3, 4, 0, 3, 4, 4, 3, 0, 4, 3, 5, 5, 3, 4, 0, 3, 4, 4, 3, 8, 4, 3, 7, 0, 3, 4, 5, 3, 4, 4, 3, 5, 4, 3, 0, 5, 3, 4, 7, 3, 4, 4, 3, 7, 4, 3, 5, 0, 3, 4, 5, 3, 4, 4, 3, 5, 4, 3, 9, 7, 3, 4, 0, 3, 4, 4, 3, 7, 4, 3, 5, 5, 3, 4, 7, 3, 4, 4, 3, 0, 4, 3, 9, 8, 3, 4, 5, 3, 4, 4, 3, 5, 4, 3, 7, 5, 3, 4, 0, 3, 4, 4, 3, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
I.e., if n is not a square, a(n) is the smallest number d for which a sequence that has a common difference of d contains n but that has no squares.
All nonzero values in this sequence are at least 3.
All nonzero values are prime powers, and every prime power except 2 appears in the sequence. This can be proved using the Chinese remainder theorem. - Franklin T. Adams-Watters, Jun 10 2011
Records of nonzero values in this sequence are in A066730.
LINKS
EXAMPLE
a(2) = 3 because there are no squares in the sequence 2, 5, 8, 11, 14, 17, 20, ...
PROG
(Python)
import math
def A139401(n):
if int(math.sqrt(n)) == math.sqrt(n):
return 0
for pp in range(2, n + 2): # only really need to check prime powers
residues = frozenset(pow(k, 2, pp) for k in range(pp))
if n % pp not in residues:
return pp # Dan Uznanski, Jun 22 2021
(PARI) a(n) = if (issquare(n), 0, my(k=2); while (issquare(Mod(n, k)), k++); k); \\ Michel Marcus, Jun 25 2021
CROSSREFS
Sequence in context: A063405 A360533 A346524 * A110061 A363804 A220956
KEYWORD
nonn
AUTHOR
J. Lowell, Jun 09 2008, Jun 10 2008
EXTENSIONS
More terms from John W. Layman, Jun 17 2008
New name from Franklin T. Adams-Watters, Jun 10 2011
STATUS
approved

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Last modified April 21 19:32 EDT 2024. Contains 371885 sequences. (Running on oeis4.)