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

1,2

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

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A005935, A015518.

Sequence in context: A348753 A276378 A243292 * A171525 A140475 A171577

Adjacent sequences: A271113 A271114 A271115 * A271117 A271118 A271119

Keyword

nonn,easy

Author

Altug Alkan, Mar 31 2016

Status

approved