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

1,1

Comments

Repunit primes in base -9. - Paul Bourdelais

Links

Table of n, a(n) for n=1..12.

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

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 *)

Prog

(PFGW v3.3.1 from primeform.net) pfgw -b2 -f10 bNeg9.txt::
ABC2 (9^$a+1)/10 // -f{4*$a}
a: primes from 3 to 1e6}
(Magma) [n: n in [0..800] | IsPrime((9^n + 1) div 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

Crossrefs

Sequence in context: A002148 A290977 A200957 * A142642 A201850 A013526

Adjacent sequences: A057172 A057173 A057174 * A057176 A057177 A057178

Keyword

nonn

Author

N. J. A. Sloane, Sep 15 2000

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

Status

approved