A271116 Integers n such that round(3^n/12) is divisible by n.

1, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 91, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307

Offset: 1

Author

Altug Alkan, Mar 31 2016

Keywords

• nonn
• easy

Comments

In other words, numbers n such that A015518(n-1) is divisible by n.

This sequence generates prime numbers except 2 and 3.

The first few composite terms in this sequence are 91, 121, 671, 703, 949. Note that they are pseudoprimes to base 3.

Also, numbers k such that 3^(k-1) mod (4*k) = 1. In the first million terms only 908 terms are nonprimes. - David A. Corneth, Oct 02 2020

Examples

			5 is a term because round(3^5/12) = 20 is divisible by 5.
6 is not a term because round(3^6/12) = 61 which is not divisible by 6. - _David A. Corneth_, Oct 02 2020
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005935, A015518.

Programs

Mathematica

Select[Range@ 308, Divisible[Round[3^#/12], #] &] (* Michael De Vlieger, Mar 31 2016 *)

PARI

f(n) = round(3^n/12);
for(n=1, 1e3, if(f(n) % n == 0, print1(n, ", ")));

PARI

is(n) = lift(Mod(3, 4*n)^(n-1))==1 \\ David A. Corneth, Oct 02 2020