A101153 Indices of primes in sequence defined by A(0) = 79, A(n) = 10*A(n-1) - 1 for n > 0.

0, 3, 17, 27, 54, 1727, 1875, 1883, 6840, 10781, 25365, 98445, 137249

Offset: 1

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 03 2004

Keywords

• nonn
• hard
• more

Comments

Numbers n such that (710*10^n + 1)/9 is a prime.

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

Numbers corresponding to terms <= 54 are certified primes.

The next term after 1883 is greater than 5000. - Ryan Propper, Jun 16 2005

Examples

			78889 is a prime, hence 3 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 788...889.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A103067.

Programs

PARI

a=79;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a-1)

PARI

for(n=0,1000,if(isprime((710*10^n+1)/9),print1(n,",")))

Formula

a(n) = A103067(n) - 1.

Extensions

3 more terms from Ryan Propper, Jun 16 2005

6840 from Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 28 2007

a(10)-a(13) from Kamada data by Ray Chandler, Apr 23 2015