A101065 Indices of primes in sequence defined by A(0) = 89, A(n) = 10*A(n-1) - 51 for n > 0.

0, 1, 3, 8, 9, 14, 43, 54, 55, 123, 139, 278, 673, 847, 1419, 1461, 3313, 3441, 4140, 35624

Offset

1,3

Comments

Numbers n such that (750*10^n + 51)/9 is prime.

Numbers n such that digit 8 followed by n >= 0 occurrences of digit 3 followed by digit 9 is prime.

Numbers corresponding to terms <= 847 are certified primes.

a(21) > 10^5. - Robert Price, Oct 20 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..20.

Makoto Kamada, Prime numbers of the form 833...339.

Index entries for primes involving repunits.

Formula

a(n) = A103078(n) - 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

Example

83339 is prime, hence 3 is a term.

Mathematica

Flatten[Position[NestList[10#-51&, 89, 4200], _?PrimeQ]-1] (* Harvey P. Dale, Apr 05 2012 *)
Select[Range[0, 100000], PrimeQ[(750*10^# + 51)/9] &] (* Robert Price, Oct 20 2015 *)

Prog

(PARI) a=89; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-51)
(PARI) for(n=0, 1500, if(isprime((750*10^n+51)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103078.

Sequence in context: A286177 A287579 A289142 * A152411 A080517 A264898

Adjacent sequences: A101062 A101063 A101064 * A101066 A101067 A101068

Keyword

nonn,hard,more

Author

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

Extensions

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

a(20) from Erik Branger May 01 2013 by Ray Chandler, Apr 29 2015

Status

approved