A101078 Indices of primes in sequence defined by A(0) = 89, A(n) = 10*A(n-1) - 11 for n > 0.

0, 2, 5, 30, 35, 60, 116, 228, 338, 3164, 3957, 5276, 5342, 6078, 6534, 8484, 15083, 34536

Offset: 1

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 30 2004

Keywords

• nonn
• hard
• more

Comments

Numbers n such that (790*10^n + 11)/9 is prime.

Numbers n such that digit 8 followed by n >= 0 occurrences of digit 7 followed by digit 9 is prime.

Numbers corresponding to terms <= 338 are certified primes.

a(19) > 10^5. - Robert Price, Oct 27 2015

Examples

			8777779 is prime, hence 5 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 877...779.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A103091.

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(790*10^# + 11)/9] &] (* Robert Price, Oct 27 2015 *)

PARI

a=89;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a-11)

PARI

for(n=0,1000,if(isprime((790*10^n+11)/9),print1(n,",")))

Formula

a(n) = A103091(n) - 1.

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(17)-a(18) from Kamada data by Ray Chandler, Apr 29 2015