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 A366973 Smallest odd prime p such that n^((p+1)/2) == n (mod p). 4
 3, 3, 7, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 13, 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, 13, 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 a(n) is the smallest odd prime p for which the Legendre symbol (n / p) >= 0. For any set S of odd primes, by Chinese Remainder Theorem, there is n such that n is a primitive root mod each prime p in S, and then n^((p-1)/2) =/= 1 (mod p). Since n is invertible mod p, n^((p-1)/2) =/= 1 (mod p) implies n^((p+1)/2) =/= n (mod p). So this sequence is unbounded. - Robert Israel, Oct 31 2023 LINKS Robin Visser, Table of n, a(n) for n = 0..10000 MAPLE f:= proc(n) local p; p:= 2; do p:= nextprime(p); if n &^ ((p+1)/2) - n mod p = 0 then return p fi od end proc: map(f, [\$0..100]); # Robert Israel, Oct 30 2023 MATHEMATICA a[n_] := Module[{p = 3}, While[PowerMod[n, (p + 1)/2, p] != Mod[n, p], p = NextPrime[p]]; p]; Array[a, 100, 0] (* Amiram Eldar, Oct 30 2023 *) PROG (PARI) a(n) = my(p=3); while(Mod(n, p)^((p+1)/2) != n, p=nextprime(p+1)); p; \\ Michel Marcus, Oct 30 2023 CROSSREFS Cf. A309316, A366930, A366982. Sequence in context: A089488 A367034 A366982 * A076560 A359048 A096915 Adjacent sequences: A366970 A366971 A366972 * A366974 A366975 A366976 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 17 23:36 EDT 2024. Contains 375991 sequences. (Running on oeis4.)