A102034 Indices of primes in sequence defined by A(0) = 17, A(n) = 10*A(n-1) + 27 for n > 0.

0, 1, 2, 3, 12, 13, 75, 236, 871, 987, 1279, 1369, 2685, 3611, 4050, 4644, 9161, 10855, 25958, 64881, 144219, 153745, 185929

Offset

1,3

Comments

Numbers n such that (180*10^n - 27)/9 is prime.

Numbers n such that digit 1 followed by n >= 0 occurrences of digit 9 followed by digit 7 is prime.

Numbers corresponding to terms <= 987 are certified primes.

a(21) > 10^5. - Robert Price, Nov 16 2014

a(24) > 2*10^5. - Robert Price, Jul 11 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..23.

Makoto Kamada, Prime numbers of the form 199...997.

Index entries for primes involving repunits.

Formula

a(n) = A102947(n) - 1. - Robert Price, Nov 16 2014

Example

197 is prime, hence 1 is a term.

Mathematica

Select[Range[0, 1000], PrimeQ[(180 10^# - 27) / 9] &] (* Vincenzo Librandi, Nov 17 2014 *)

Prog

(PARI) a=17; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+27)
(PARI) for(n=0, 1500, if(isprime((180*10^n-27)/9), print1(n, ", ")))
(Magma) [n: n in [0..500] | IsPrime((180*10^n-27) div 9) ]; // Vincenzo Librandi, Nov 17 2014

Crossrefs

Cf. A000533, A002275, A102947.

Sequence in context: A081347 A309176 A074347 * A102150 A039588 A024579

Adjacent sequences: A102031 A102032 A102033 * A102035 A102036 A102037

Keyword

nonn,hard,more

Author

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

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(18)-a(20) derived from A102947 by Robert Price, Nov 16 2014

a(21)-a(23) from Robert Price, Jul 11 2015

Status

approved