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

1,2

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.

References

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

Links

Table of n, a(n) for n=1..6.

Patrick De Geest, PDP Reference Table - 929.

Makoto Kamada, Prime numbers of the form 922...229.

Index entries for primes involving repunits.

Formula

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

Example

9222229 is prime, hence 5 is a term.

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 *)

Prog

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

Crossrefs

Cf. A000533, A002275, A068651, A082718.

Sequence in context: A236509 A330488 A057178 * A302144 A041909 A041048

Adjacent sequences: A056262 A056263 A056264 * A056266 A056267 A056268

Keyword

hard,nonn,more

Author

Robert G. Wilson v, Aug 18 2000

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

Status

approved