A102008 Indices of primes in sequence defined by A(0) = 19, A(n) = 10*A(n-1) - 81 for n > 0.

0, 1, 2, 3, 8, 17, 21, 44, 48, 55, 68, 145, 201, 271, 2729, 2840, 4561, 31809, 43185, 48108, 92690

Offset

1,3

Comments

Numbers n such that 10*10^n + 9 is prime.

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

Numbers corresponding to terms <= 271 are certified primes.

a(22) > 2*10^5. - Robert Price, Oct 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..21.

Makoto Kamada, Prime numbers of the form 100...009.

Formula

a(n) = A088275(n) - 1.

Example

1009 is prime, hence 2 is a term.

Mathematica

Select[Range[0, 200000], PrimeQ[10*10^# + 9] &] (* Robert Price, Oct 11 2015 *)

Prog

(PARI) a=19; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-81)
(PARI) for(n=0, 1500, if(isprime(10*10^n + 9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A088275.

Sequence in context: A277346 A005648 A113947 * A200083 A210701 A158921

Adjacent sequences: A102005 A102006 A102007 * A102009 A102010 A102011

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(21) from Kamada data by Ray Chandler, May 01 2015

Status

approved