A101136 Indices of primes in sequence defined by A(0) = 79, A(n) = 10*A(n-1) - 61 for n > 0.

0, 2, 3, 6, 8, 12, 32, 36, 75, 146, 296, 1850, 3456, 3608, 45218

Offset: 1

Author

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

Keywords

• nonn
• hard
• more

Comments

Numbers n such that (650*10^n + 61)/9 is prime.

Numbers n such that digit 7 followed by n >= 0 occurrences of digit 2 followed by digit 9 is prime.

Numbers corresponding to terms <= 296 are certified primes.

a(16) > 10^5. - Robert Price, Oct 01 2015

All a(n) == 0, 2 or 3 mod 6 (cf. A047244). - Robert Israel, Oct 01 2015

Examples

			72222229 is prime, hence 6 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 722...229.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A103054.

Programs

Magma

[n: n in [0..3*10^2]| IsPrime((650*10^n+61) div 9)]; // Vincenzo Librandi, Oct 02 2015

Maple

select(t -> isprime((650*10^t + 61)/9), [seq(seq(6*s+i,i=[0,2,3]),s=0..700)]); # Robert Israel, Oct 01 2015

Mathematica

Select[Range[0, 100000], PrimeQ[(650*10^# + 61)/9] &] (* Robert Price, Oct 01 2015 *)

PARI

a=79;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a-61)

PARI

for(n=0,1000,if(isprime((650*10^n+61)/9),print1(n,",")))

Formula

a(n) = A103054(n) - 1.

Extensions

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

a(15) from Erik Branger May 01 2013 by Ray Chandler, Apr 30 2015