A015949 Numbers k such that k | 3^k + 1.

1, 2, 10, 50, 250, 1250, 5050, 6250, 11810, 25250, 31250, 59050, 126250, 156250, 295250, 510050, 631250, 750250, 781250, 1476250, 2125250, 2550250, 3156250, 3751250, 3906250, 5964050, 7381250, 10626250, 12751250, 13947610, 15781250

Offset: 1

Author

Robert G. Wilson v

Keywords

• nonn

Comments

a(n) mod 20 = 10 for n >= 3. - G. C. Greubel, Nov 05 2018

This sequence is infinite, because for n > 1, 3^a(n) + 1 is in this sequence. - Jinyuan Wang, Nov 06 2018

For the provided data, if k is a term then p*k is a term where p is an odd divisor of k. - David A. Corneth, Nov 06 2018

Links

• Giovanni Resta, Table of n, a(n) for n = 1..180 (first 100 terms from G. C. Greubel)

Crossrefs

Cf. A034472 (3^n+1).

Cf. A006521 (k | 2^k + 1), A015950 (k | 4^k + 1), A015951 (k | 5^k + 1).

Column k=3 of A333429.

Programs

Magma

[n: n in [1..2*10^7]| Modexp(3, n, n)+1 eq n]; // Vincenzo Librandi, Nov 01 2018

Mathematica

Do[If[PowerMod[3, n, n] + 1 == n, Print[n]], {n, 1, 10^7}] (* Jinyuan Wang, Nov 01 2018 *)
Select[Range[16*10^6],PowerMod[3,#,#]==#-1&] (* Harvey P. Dale, Dec 15 2024 *)

PARI

for(n=1, 10^7, if(Mod(3, n)^n==-1, print1(n, ", "))) \\ Jinyuan Wang, Nov 01 2018

Extensions

Corrected by David W. Wilson