A101130 Indices of primes in sequence defined by A(0) = 79, A(k) = 10*A(k-1) - 81 for k > 0.

0, 1, 3, 5, 10, 11, 12, 34, 45, 56, 127, 155, 262, 352, 395, 428, 782, 981, 1057, 1562, 1694, 1815, 1936, 4235, 4430, 6857, 9897, 13144, 16645, 20890, 63350, 105295, 113692, 121143, 163779, 234914, 284750

Offset: 1

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 03 2004

Keywords

• nonn
• hard
• more

Comments

Numbers k such that 70*10^k + 9 is prime.

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

Numbers corresponding to terms <= 981 are certified primes.

a(38) > 3*10^5. - Robert Price, Jul 10 2023

Examples

			70009 is prime, hence 3 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 700...009.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A097954.

Programs

Magma

[n: n in [0..400] |IsPrime(70*10^n + 9)]; // Vincenzo Librandi, Sep 06 2015

Mathematica

Select[Range[0, 300], PrimeQ[70*10^# + 9] &] (* Robert Price, Sep 05 2015 *)

PARI

a=79;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-81)

PARI

for(n=0,1500,if(isprime(70*10^n+9),print1(n,",")))

Formula

a(n) = A097954(n) - 1.

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(28)-a(31) from Kamada data by Ray Chandler, Apr 29 2015

a(32)-a(35) from Robert Price, Sep 05 2015

a(36)-a(37) from Robert Price, Jul 10 2023