A056250 Indices of primes in sequence defined by A(0) = 11, A(n) = 10*A(n-1) + 81 for n > 0.

0, 1, 3, 7, 39, 85, 199, 729, 1459, 23671, 28629

Offset: 1

Author

Robert G. Wilson v, Aug 18 2000

Keywords

• nonn
• hard
• more

Comments

Numbers n such that (180*10^n - 81)/9 is prime.

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

Numbers corresponding to terms <= 1459 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.

Examples

			191 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

• Tony Crilly, A family of discrete spirals, The Mathematical Gazette (2020) Vol. 104, Issue 560, 215-224.
• Patrick De Geest, PDP Reference Table - 191.
• Makoto Kamada, Prime numbers of the form 199...991.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A068649, A082703.

Programs

Mathematica

Select[Range[0, 2000], PrimeQ[(180 10^# - 81) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)

PARI

a=11;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+81)

PARI

for(n=0,1500,if(isprime((180*10^n-81)/9),print1(n,",")))

Formula

a(n) = A082703(n-1) - 2 for n > 1.

Extensions

Additional comments from Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004

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

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

Updated comments section and a link, by Patrick De Geest, Nov 02 2014

Edited by Ray Chandler, Nov 04 2014