A276740 Numbers n such that 3^n == 5 (mod n).

1, 2, 4, 76, 418, 1102, 4687, 7637, 139183, 2543923, 1614895738, 9083990938, 23149317409, 497240757797, 4447730232523, 16000967516764, 65262766108619, 141644055557882

Offset

1,2

Comments

No other terms below 10^15. Some larger terms: 194995887252090239, 2185052151122686482926861593785262. - Max Alekseyev, Oct 13 2016

Links

Table of n, a(n) for n=1..18.

Example

3 == 5 (mod 1), so 1 is a term;
9 == 5 (mod 2), so 2 is a term.

Mathematica

Select[Range[10^7], PowerMod[3, #, #] == Mod[5, #] &] (* Michael De Vlieger, Sep 26 2016 *)

Prog

(PARI) isok(n) = Mod(3, n)^n == Mod(5, n); \\ Michel Marcus, Sep 17 2016
(Python)
A276740_list = [1, 2, 4]+[n for n in range(5, 10**6) if pow(3, n, n) == 5] # Chai Wah Wu, Oct 04 2016

Crossrefs

Cf. A066601.

Solutions to 3^n == k (mod n): A277340 (k=-11), A277289 (k=-7), A277288 (k=-5), A015973 (k=-2), A015949 (k=-1), A067945 (k=1), A276671 (k=2), this sequence (k=5), A277628 (k=6), A277126 (k=7), A277630 (k=8), A277274 (k=11).

Sequence in context: A053550 A018378 A023175 * A006688 A292711 A018389

Adjacent sequences: A276737 A276738 A276739 * A276741 A276742 A276743

Keyword

nonn,more

Author

Dmitry Ezhov, Sep 16 2016

Extensions

a(11)-a(13) from Chai Wah Wu, Oct 05 2016

a(14) from Lars Blomberg, Oct 12 2016

a(15)-a(18) from Max Alekseyev, Oct 13 2016

a(12) was missing Robert G. Wilson v, Oct 19 2016

Status

approved