login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A056264 Indices of primes in sequence defined by A(0) = 99, A(n) = 10*A(n-1) - 71 for n > 0. 1

%I

%S 1,245,1139,10393,43879

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

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

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

%C Numbers corresponding to terms <= 1139 are certified primes. For number corresponding to 10393 and larger see P. De Geest, PDP Reference Table.

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

%H Patrick De Geest, <a href="http://www.worldofnumbers.com/deplat.htm#pdp919">PDP Reference Table - 919</a>.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/9/91119.htm#prime">Prime numbers of the form 911...119</a>.

%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.

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

%e 919 is prime, hence 1 is a term.

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

%o (PARI) a=99;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-71)

%o (PARI) for(n=0,1500,if(isprime((820*10^n+71)/9),print1(n,",")))

%Y Cf. A000533, A002275, A082717.

%K nonn,hard

%O 1,2

%A _Robert G. Wilson v_, Aug 18 2000

%E Additional comments from _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004

%E Edited by _N. J. A. Sloane_, Jun 15 2007

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

%E Edited comments section by _Patrick De Geest_, Nov 02 2014

%E Edited by _Ray Chandler_, Nov 04 2014

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 29 10:06 EDT 2020. Contains 337428 sequences. (Running on oeis4.)