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

Author

Dmitry Ezhov, Sep 16 2016

Keywords

• nonn
• more

Comments

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

Examples

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

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).

Programs

Mathematica

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

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

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