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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
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
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.)