A222948 Numbers k such that 3*k+1 divides 3^k+1.

0, 1, 9, 3825, 6561, 102465, 188505, 190905, 1001385, 1556985, 3427137, 5153577, 5270625, 5347881, 13658225, 14178969, 20867625, 23828049, 27511185, 29400657, 48533625, 80817009, 83406609, 89556105, 108464265, 123395265, 127558881, 130747689, 133861905

Offset: 1

Author

Jonathan Vos Post, Apr 07 2013

Keywords

• nonn

Comments

This is to 3 as A224486 is to 2

Displayed terms complete up to 200*10^6. - Joerg Arndt, Apr 08 2013

Examples

			0 is a term because (3^0+1)/(3*0+1) = 2.
1 is a term because (3^1+1)/(3*1+1) = 1.
9 is a term because (3^9+1)/(3*9+1) = 703.
		

Links

• Joerg Arndt, Table of n, a(n) for n = 1..64 (all terms <= 10^9)

Crossrefs

Cf. A224486 (k such that 2*k+1 divides 2^k+1).

Cf. A000244, A016777.

Programs

PARI

for(n=0,10^9,if((3^n+1)%(3*n+1)==0,print1(n,", "))); /* Joerg Arndt, Apr 08 2013 */
/* the following program is significantly faster; it gives terms >=1: */

PARI

for(n=0, 10^12, my(m=3*n+1); if( Mod(3,m)^n==Mod(-1,m), print1(n, ", ") ) ); /* Joerg Arndt, Apr 08 2013 */

Formula

{n such that (1+A000244(n))/A016777(n) is an integer}.

Extensions

Terms > 9 from Joerg Arndt, Apr 08 2013