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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 Dan Uznanski, Table of n, a(n) for n = 1..10000 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 Cf. A066730, A100867, A144294, A354597. Sequence in context: A063405 A360533 A346524 * A110061 A363804 A220956 Adjacent sequences: A139398 A139399 A139400 * A139402 A139403 A139404 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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