A102031 Indices of primes in sequence defined by A(0) = 19, A(n) = 10*A(n-1) - 1 for n > 0.

0, 2, 11, 266, 842, 6299, 37991, 54116, 121241, 121620

Offset

1,2

Comments

Numbers n such that (170*10^n + 1)/9 is prime.

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

Numbers corresponding to terms <= 842 are certified primes.

a(11) > 2*10^5. - Robert Price, Nov 16 2014

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..10.

Makoto Kamada, Prime numbers of the form 188...889.

Index entries for primes involving repunits.

Formula

a(n) = A102945(n) - 1.

Example

1889 is prime, hence 2 is a term.

Maple

A102031:=n->`if`(isprime((170*10^n+1)/9), n, NULL): seq(A102031(n), n=0..10^3); # Wesley Ivan Hurt, Nov 16 2014

Mathematica

Select[Range[0, 10^3], PrimeQ[(170*10^# + 1)/9] &] (* Wesley Ivan Hurt, Nov 16 2014 *)

Prog

(PARI) a=19; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-1)
(PARI) for(n=0, 1500, if(isprime((170*10^n+1)/9), print1(n, ", ")))
(Magma) [n: n in [0..300] | IsPrime((170*10^n+1) div 9)]; // Vincenzo Librandi, Nov 17 2014

Crossrefs

Cf. A000533, A002275, A102945.

Sequence in context: A343898 A134096 A132571 * A248865 A072386 A185122

Adjacent sequences: A102028 A102029 A102030 * A102032 A102033 A102034

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004

Extensions

6299 from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 22 2007

a(7)-a(10) added by Max Alekseyev, Dec 12 2011

Status

approved