A125774 Numbers k such that 3^k mod k = 3^k mod k^2.

1, 2, 3, 4, 9, 11, 20, 22, 27, 33, 81, 99, 220, 243, 644, 729, 1220, 2187, 2420, 5060, 6561, 7128, 8368, 13420, 14740, 19683, 23620, 40573, 55660, 59049, 145420, 147620, 162140, 177147, 237820, 259820, 290620, 308660, 339020, 447740, 531441, 548660

Offset: 1

Author

Alexander Adamchuk, Dec 07 2006

Keywords

• nonn

Comments

This sequence includes all powers of 3. a(2) = 2, a(3) = 3, a(6) = 11 and a(45) = 1006003 are the only known primes in this sequence.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..400 (terms 1..100 from Harvey P. Dale)

Crossrefs

Cf. A014127 (Primes p such that p^2 divides 3^(p-1) - 1).

Cf. A068535 (Numbers k such that 2^k mod k = 2^k mod k^2).

Cf. A125773 (Numbers k, that are not powers of 2, such that 2^k mod k = 2^k mod k^2).

Cf. A125775 (Numbers k such that 5^k mod k = 5^k mod k^2).

Programs

Mathematica

Do[f=PowerMod[3,n,n];g=PowerMod[3,n,n^2];If[f==g,Print[n]],{n,1,1100000}]
Select[Range[600000],PowerMod[3,#,#]==PowerMod[3,#,#^2]&] (* Harvey P. Dale, Feb 21 2013 *)