A056264 Indices of primes in sequence defined by A(0) = 99, A(n) = 10*A(n-1) - 71 for n > 0.

1, 245, 1139, 10393, 43879

Offset

1,2

Comments

Numbers n such that (820*10^n + 71)/9 is a prime.

Numbers n such that digit 9 followed by n >= 0 occurrences of digit 1 followed by digit 9 is prime.

Numbers corresponding to terms <= 1139 are certified primes. For number corresponding to 10393 and larger 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..5.

Patrick De Geest, PDP Reference Table - 919.

Makoto Kamada, Prime numbers of the form 911...119.

Index entries for primes involving repunits.

Formula

a(n) = A082717(n) - 2.

Example

919 is prime, hence 1 is a term.

Mathematica

Flatten[Position[NestList[10#-71&, 99, 1200], _?PrimeQ]]-1 (* Harvey P. Dale, May 02 2012 *)

Prog

(PARI) a=99; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-71)
(PARI) for(n=0, 1500, if(isprime((820*10^n+71)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A082717.

Sequence in context: A350421 A236887 A237161 * A154080 A259511 A023097

Adjacent sequences: A056261 A056262 A056263 * A056265 A056266 A056267

Keyword

nonn,hard

Author

Robert G. Wilson v, Aug 18 2000

Extensions

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

Edited by N. J. A. Sloane, Jun 15 2007

One more term from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

Edited comments section by Patrick De Geest, Nov 02 2014

Edited by Ray Chandler, Nov 04 2014

Status

approved