A101060 Indices of primes in sequence defined by A(0) = 89, A(n) = 10*A(n-1) - 71 for n > 0.

0, 3, 6, 8, 18, 21, 69, 101, 120, 122, 234, 359, 593, 1613, 2409, 16047, 16173

Offset

1,2

Comments

Numbers n such that (730*10^n + 71)/9 is prime.

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

Numbers corresponding to terms <= 593 are certified primes.

a(18) > 10^5. - Robert Price, Oct 13 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..17.

akoto Kamada, Prime numbers of the form 811...119.

Index entries for primes involving repunits.

Formula

a(n) = A103073(n) - 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

Example

81119 is prime, hence 3 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(730*10^# + 71)/9] &] (* Robert Price, Oct 13 2015 *)

Prog

(PARI) a=89; for(n=0, 1000, if(isprime(a), print1(n, ", ")); a=10*a-71)
(PARI) for(n=0, 1000, if(isprime((730*10^n+71)/9), print1(n, ", ")))
(Magma) [n: n in [0..400] | IsPrime((730*10^n+71) div 9)]; // Vincenzo Librandi, Oct 14 2015

Crossrefs

Cf. A000533, A002275, A103073.

Sequence in context: A253855 A298860 A068979 * A278486 A038064 A093899

Adjacent sequences: A101057 A101058 A101059 * A101061 A101062 A101063

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

Status

approved