A102031 Indices of primes in sequence defined by A(0) = 19, A(n) = 10*A(n-1) - 1 for n > 0.

0, 2, 11, 266, 842, 6299, 37991, 54116, 121241, 121620

Offset: 1

Author

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

Keywords

• nonn
• hard
• more

Comments

Numbers n such that (170*10^n + 1)/9 is prime.

Numbers n such that digit 1 followed by n >= 0 occurrences of digit 8 followed by digit 9 is prime.

Numbers corresponding to terms <= 842 are certified primes.

a(11) > 2*10^5. - Robert Price, Nov 16 2014

Examples

			1889 is prime, hence 2 is a term.
		

References

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

Links

• Makoto Kamada, Prime numbers of the form 188...889.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A102945.

Programs

Magma

[n: n in [0..300] | IsPrime((170*10^n+1) div 9)]; // Vincenzo Librandi, Nov 17 2014

Maple

A102031:=n->`if`(isprime((170*10^n+1)/9), n, NULL): seq(A102031(n), n=0..10^3); # Wesley Ivan Hurt, Nov 16 2014

Mathematica

Select[Range[0, 10^3], PrimeQ[(170*10^# + 1)/9] &] (* Wesley Ivan Hurt, Nov 16 2014 *)

PARI

a=19;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-1)

PARI

for(n=0,1500,if(isprime((170*10^n+1)/9),print1(n,",")))

Formula

a(n) = A102945(n) - 1.

Extensions

6299 from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 22 2007

a(7)-a(10) added by Max Alekseyev, Dec 12 2011