A101016 Indices of primes in sequence defined by A(0) = 91, A(n) = 10*A(n-1) + 71 for n > 0.

5, 8, 89, 110, 209, 236, 413, 1191, 1259, 5835, 6771, 24860, 52430

Offset

1,1

Comments

Numbers n such that (890*10^n - 71)/9 is prime.

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

Numbers corresponding to terms <= 413 are certified primes.

Certified primality of terms corresponding to 1191 and 1259 with Primo. - Ryan Propper, Jun 20 2005

a(14) > 10^5. - Robert Price, Nov 12 2015

References

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

Links

Table of n, a(n) for n=1..13.

Makoto Kamada, Prime numbers of the form 988...881.

Index entries for primes involving repunits.

Formula

a(n) = A103107(n+1) - 1.

Example

9888881 is prime, hence 5 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(890*10^# - 71)/9] &] (* Robert Price, Nov 12 2015 *)

Prog

(PARI) a=91; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+71)
(PARI) for(n=0, 1500, if(isprime((890*10^n-71)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103107.

Sequence in context: A260695 A153720 A372124 * A264295 A025518 A361225

Adjacent sequences: A101013 A101014 A101015 * A101017 A101018 A101019

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004

Extensions

Two additional terms, corresponding to probable primes, from Ryan Propper, Jun 20 2005

Edited by T. D. Noe, Oct 30 2008

a(12) from Kamada data by Ray Chandler, Apr 29 2015

a(13) from Robert Price, Nov 12 2015

Status

approved