A101064 Indices of primes in sequence defined by A(0) = 89, A(n) = 10*A(n-1) - 61 for n > 0.

0, 1, 4, 7, 13, 54, 102, 330, 1066, 13710, 24396, 54582

Offset

1,3

Comments

Numbers n such that (740*10^n + 61)/9 is prime.

Numbers n such that digit 8 followed by n >= 0 occurrences of digit 2 followed by digit 9 is prime.

Numbers corresponding to terms <= 1066 are certified primes.

a(13) > 10^5. - Robert Price, Oct 26 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..12.

Makoto Kamada, Prime numbers of the form 822...229.

Index entries for primes involving repunits.

Formula

a(n) = A103077(n) - 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

Example

822229 is prime, hence 4 is a term.

Mathematica

Flatten[Position[NestList[10#-61&, 89, 1100], _?PrimeQ]]-1 (* Harvey P. Dale, Aug 16 2014 *)
Select[Range[0, 100000], PrimeQ[(740*10^# + 61)/9] &] (* Robert Price, Oct 26 2015 *)

Prog

(PARI) a=89; for(n=0, 1200, if(isprime(a), print1(n, ", ")); a=10*a-61)
(PARI) for(n=0, 1200, if(isprime((740*10^n+61)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103077.

Sequence in context: A122552 A197546 A074862 * A243707 A347137 A347413

Adjacent sequences: A101061 A101062 A101063 * A101065 A101066 A101067

Keyword

nonn,hard,more

Author

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

Extensions

a(10)-a(11) from Kamada data by Ray Chandler, Apr 29 2015

a(12) from Robert Price, Oct 26 2015

Status

approved