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 A366982 a(n) is the smallest odd k > 1 such that n^((k+1)/2) == n (mod k). 2
 3, 3, 7, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 9, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 11, 3, 3, 5, 3, 3, 5, 3, 3, 11, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 9, 3, 3, 5, 3, 3, 13, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 17, 3, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS If this sequence is bounded, then it is periodic with period P = LCM(A), where A is the set of all (pairwise distinct) terms. Note that n^((1729+1)/2) == n (mod 1729) for every n >= 0, where 1729 is the smallest absolute Euler pseudoprime (A033181). Thus a(n) <= 1729. So, as said, this sequence is periodic. What is its period? If the largest term of this sequence is indeed 1729, it should be expected that its period P may be longer than the period of Euler primary pretenders (A309316), namely P > 41#*571#/4 (248 digits). LINKS Table of n, a(n) for n=0..85. MATHEMATICA a[n_] := Module[{k = 3}, While[PowerMod[n, (k + 1)/2, k] != Mod[n, k], k += 2]; k]; Array[a, 100, 0] (* Amiram Eldar, Oct 30 2023 *) PROG (PARI) a(n) = my(k=3); while (Mod(n, k)^((k+1)/2) != n, k+=2); k; \\ Michel Marcus, Oct 31 2023 CROSSREFS Cf. A033181, A309316, A366930, A366973. Sequence in context: A333339 A089488 A367034 * A366973 A076560 A359048 Adjacent sequences: A366979 A366980 A366981 * A366983 A366984 A366985 KEYWORD nonn AUTHOR Thomas Ordowski, Oct 30 2023 EXTENSIONS More terms from Amiram Eldar, Oct 30 2023 STATUS approved

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Last modified September 10 09:32 EDT 2024. Contains 375786 sequences. (Running on oeis4.)