A101067 Indices of primes in sequence defined by A(0) = 83, A(n) = 10*A(n-1) + 13 for n > 0.

0, 2, 3, 9, 14, 24, 68, 158, 165, 260, 441, 1338, 1796, 2169, 3162, 3471, 4916, 18266

Offset

1,2

Comments

Numbers n such that (760*10^n - 13)/9 is a prime.

Numbers n such that digit 8 followed by n >= 0 occurrences of digit 4 followed by digit 3 is prime.

Numbers corresponding to terms <= 441 are certified primes.

a(19) > 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..18.

Makoto Kamada, Prime numbers of the form 844...443.

Index entries for primes involving repunits.

Formula

a(n) = A103080(n+1) - 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008; adapted to offset by Robert Price, Oct 21 2015

Example

84443 is prime, hence 3 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(760*10^# - 13)/9] &] (* Robert Price, Oct 20 2015 *)

Prog

(PARI) a=83; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+13)
(PARI) for(n=0, 1500, if(isprime((760*10^n-13)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103080.

Sequence in context: A338234 A048038 A113501 * A056645 A295857 A047171

Adjacent sequences: A101064 A101065 A101066 * A101068 A101069 A101070

Keyword

nonn,hard,more

Author

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

Extensions

5 more terms from Ryan Propper, Jun 18 2005

a(18) from Kamada data by Ray Chandler, Apr 29 2015

Status

approved