A056265 Indices of primes in sequence defined by A(0) = 99, A(n) = 10*A(n-1) - 61 for n > 0.

1, 5, 11, 109, 3607, 37783

Offset: 1

Author

Robert G. Wilson v, Aug 18 2000

Keywords

• hard
• nonn
• more

Comments

Numbers n such that (830*10^n + 61)/9 is prime. - Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004

Numbers n such that digit 9 followed by n >= 0 occurrences of digit 2 followed by digit 9 is prime.

Numbers corresponding to terms <= 3607 are certified primes. For number corresponding to 37783 see P. De Geest, PDP Reference Table.

Examples

			9222229 is prime, hence 5 is a term.
		

References

• Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Links

• Patrick De Geest, PDP Reference Table - 929.
• Makoto Kamada, Prime numbers of the form 922...229.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A068651, A082718.

Programs

Magma

[n: n in [0..1000] | IsPrime((830*10^n + 61) div 9)]; // Vincenzo Librandi, Nov 02 2014

Mathematica

Do[If[PrimeQ[(9*10^n + 2*(10^n - 1)/9)*10 + 9], Print[n]], {n, 1, 2500}]
Select[Range[2000], PrimeQ[(830 10^# + 61) / 9] &] (* Vincenzo Librandi, Nov 02 2014 *)

PARI

a=99;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a-61) \\ Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004

PARI

for(n=0,1000,if(isprime((830*10^n + 61)/9),print1(n,","))) \\ Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004

Formula

a(n) = A082718(n) - 2.

Extensions

3607 from Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004

37783 from Patrick De Geest, Jun 26 2005

Edited by N. J. A. Sloane, Jan 14 2008

Edited by Ray Chandler, Oct 20 2010

Comments section edited by Patrick De Geest, Nov 02 2014

Editied by Ray Chandler, Nov 05 2014