A101519 Indices of primes in sequence defined by A(0) = 63, A(n) = 10*A(n-1) - 17 for n > 0.

1, 2, 4, 10, 11, 22, 74, 100, 121, 172, 646, 2014, 2683, 11699, 19624

Offset

1,2

Comments

Numbers n such that (550*10^n + 17)/9 is prime.

Numbers n such that digit 6 followed by n >= 0 occurrences of digit 1 followed by digit 3 is prime.

Numbers corresponding to terms <= 646 are certified primes.

a(16) > 10^5 - Robert Price, Sep 09 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..15.

Makoto Kamada, Prime numbers of the form 611...113.

Index entries for primes involving repunits.

Formula

a(n) = A103027(n) - 1.

Example

611113 is prime, hence 4 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(550*10^# + 17)/9] &] (* Robert Price, Sep 09 2015 *)

Prog

(PARI) a=63; for(n=0, 1000, if(isprime(a), print1(n, ", ")); a=10*a-17)
(PARI) for(n=0, 1000, if(isprime((550*10^n+17)/9), print1(n, ", ")))
(Magma) [n: n in [0..500]| IsPrime((550*10^n + 17) div 9)]; // Vincenzo Librandi, Sep 10 2015

Crossrefs

Cf. A000533, A002275, A103027.

Sequence in context: A136818 A293556 A029984 * A227204 A249446 A184815

Adjacent sequences: A101516 A101517 A101518 * A101520 A101521 A101522

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 06 2004

Extensions

More terms from Stefan Steinerberger, May 06 2007

a(14)-a(15) from Kamada data by Ray Chandler, Apr 30 2015

Status

approved