A000236 Maximum m such that there are no two adjacent elements belonging to the same n-th power residue class modulo some prime p in the sequence 1,2,...,m (equivalently, there is no n-th power residue modulo p in the sequence 1/2,2/3,...,(m-1)/m). (Formerly M2737 N1099)

3, 8, 20, 44, 80, 343, 288, 608, 1023, 2848, 4095, 40959, 16383, 32768, 11375, 655360, 262143, 3670016, 1048575, 2097151

Offset

2,1

Comments

Rabung and Jordan (1970) incorrectly computed a(8) as 399: their placement of residues supporting a(8)=399 fails since 80 and 81 fall into the same 8th-power residue class. - Max Alekseyev, Aug 10 2005

Don Reble pointed out that for even n, the n-th residue class placement of prime factors q of n must obey the quadratic reciprocity law: q must be in an even class whenever n*(q-1) is a multiple of 8. - Max Alekseyev, Sep 04 2017

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=2..21.

J. H. Jordan, Pairs of consecutive power residues or nonresidues, Canad. J. Math., 16 (1964), 310-314.

J. R. Rabung and J. H. Jordan, Consecutive power residues or nonresidues, Math. Comp., 24 (1970), 737-740.

Formula

If 8|n, a(n) >= 2^(n/2) - 1; otherwise a(n) >= 2^n - 1. - Max Alekseyev, Aug 10 2005; corrected Sep 04, 2017.

Crossrefs

Cf. A000445, A111931.

Sequence in context: A139488 A028307 A027298 * A109327 A192982 A096585

Adjacent sequences: A000233 A000234 A000235 * A000237 A000238 A000239

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

a(8) corrected and a(9)-a(16) added by Max Alekseyev, Aug 10 2005

a(8), a(10), a(16) corrected, and a(17)-a(21) added by Don Reble, communicated by Max Alekseyev, Sep 04 2017

Status

approved