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 A188384 Primes for which there are not three consecutive nonzero quintic residues. 1
 11, 31, 41, 61, 71, 101, 131, 151, 181, 251, 311, 401, 491, 541, 571, 601, 631, 701, 761, 941, 971, 1531, 1811, 2311, 2411, 2731, 3331 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS For prime p, the quintic residues (mod p) are the positive numbers x = k^5 (mod p) for some k. For primes p = 1 (mod 5), there are (p-1)/5 nonzero quintic residues; for all other primes, there are p-1 nonzero quintic residues. Lehmer states that all primes greater than 3331 have three consecutive nonzero quintic residues. LINKS Table of n, a(n) for n=1..27. Lehmer D.H., Mechanized mathematics, Bull. Amer. Math. Soc., Vol. 72 (1966), No. 5, 739-759. MATHEMATICA ps1=Select[Prime[Range[1000]], Mod[#, 5]==1&]; noConsec={}; Do[r=Union[Table[Mod[n^5, p], {n, p-1}]]; pos=Flatten[Position[Partition[Differences[r, 1], 2, 1], {1, 1}]]; If[pos=={}, AppendTo[noConsec, p]], {p, ps1}]; noConsec CROSSREFS Cf. A184986 (quintic residues mod 3331) Sequence in context: A030430 A059313 A040975 * A040172 A040160 A040981 Adjacent sequences: A188381 A188382 A188383 * A188385 A188386 A188387 KEYWORD nonn,fini,full AUTHOR T. D. Noe, Mar 29 2011 STATUS approved

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Last modified February 26 16:21 EST 2024. Contains 370352 sequences. (Running on oeis4.)