A188384 Primes for which there are not three consecutive nonzero quintic residues.

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

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