A057175 Numbers n such that (9^n + 1)/10 is a prime.

3, 59, 223, 547, 773, 1009, 1823, 3803, 49223, 193247, 703393, 860029

Offset: 1

Author

N. J. A. Sloane, Sep 15 2000

Keywords

• nonn

Comments

Repunit primes in base -9. - Paul Bourdelais

Links

• P. Bourdelais, A Generalized Repunit Conjecture
• H. Dubner and T. Granlund, Primes of the Form (b^n+1)/(b+1), J. Integer Sequences, 3 (2000), #P00.2.7.
• H. Lifchitz, Mersenne and Fermat primes field
• Eric Weisstein's World of Mathematics, Repunit

Programs

Magma

[n: n in [0..800] | IsPrime((9^n + 1) div 10 )]; // Vincenzo Librandi, Aug 03 2015

Mathematica

lst={};Do[p=(9^n+1)/10;If[PrimeQ[p], AppendTo[lst, n]], {n, 7!}];lst (* Vladimir Joseph Stephan Orlovsky, Sep 29 2008 *)
Select[Range[4000], PrimeQ[(9^# + 1)/10] &] (* Vincenzo Librandi, Aug 03 2015 *)

PARI

first(m)=my(v=vector(m));t=0;for(i=1,m,while(!isprime((9^t + 1)\10),t++);v[i]=t;t++;);v; \\ Anders Hellström, Aug 16 2015

Extensions

a(9) corresponds to a probable prime, was discovered on Oct 22 2007. Trial factored to 1E11 with Fermat base 2 primality test. - Paul Bourdelais

a(10) corresponds to a probable prime, discovered by Paul Bourdelais, Feb 01 2010

a(11) corresponds to a probable prime, discovered by Paul Bourdelais, Aug 03 2015

a(12) corresponds to a probable prime, discovered by Paul Bourdelais, Sep 23 2020