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

Author

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

Keywords

• nonn
• hard
• more

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

Examples

			1009 is prime, hence 2 is a term.
		

References

• Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Links

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

Crossrefs

Cf. A000533, A002275, A088275.

Programs

Mathematica

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

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,",")))

Formula

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

Extensions

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

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