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

Author

Robert G. Wilson v, Aug 18 2000

Keywords

• nonn
• hard

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.

Examples

			919 is prime, hence 1 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 - 919.
• Makoto Kamada, Prime numbers of the form 911...119.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A082717.

Programs

Mathematica

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

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,",")))

Formula

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

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