A101058 Indices of primes in sequence defined by A(0) = 83, A(n) = 10*A(n-1) - 17 for n > 0.

0, 9, 23, 198, 744, 7752, 17937, 21318, 24947, 26118, 29453, 51888, 62823, 88104

Offset

1,2

Comments

Numbers n such that (730*10^n + 17)/9 is prime.

Numbers n such that digit 8 followed by n >= 0 occurrences of digit 1 followed by digit 3 is prime.

Numbers corresponding to terms <= 744 are certified primes.

a(15) > 10^5. - Robert Price, Oct 16 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..14.

Makoto Kamada, Prime numbers of the form 811...113.

Index entries for primes involving repunits.

Formula

a(n) = A103071(n) - 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

Example

81111111113 is prime, hence 9 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(730*10^# + 17)/9] &] (* Robert Price, Oct 16 2015 *)

Prog

(PARI) a=83; for(n=0, 1000, if(isprime(a), print1(n, ", ")); a=10*a-17)
(PARI) for(n=0, 1000, if(isprime((730*10^n+17)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103071.

Sequence in context: A339439 A266238 A066008 * A247960 A347559 A161431

Adjacent sequences: A101055 A101056 A101057 * A101059 A101060 A101061

Keyword

nonn,hard,more

Author

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

Extensions

7752 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(7)-a(11) from Kamada data by Ray Chandler, Apr 29 2015

a(12)-a(14) from Robert Price, Oct 16 2015

Status

approved