A056259 Indices of primes in sequence defined by A(0) = 77, A(n) = 10*A(n-1) - 13 for n > 0.

1, 3, 9, 19, 21, 57, 73, 81, 207, 349, 421, 3811, 3981, 20923, 23785, 38851, 56041, 68503, 74433

Offset: 1

Author

Robert G. Wilson v, Aug 18 2000

Keywords

• nonn
• hard
• more

Comments

Numbers n such that (680*10^n + 13)/9 is prime.

Numbers n such that digit 7 followed by n >= 0 occurrences of digit 5 followed by digit 7 is prime.

Numbers corresponding to terms <= 3981 are certified primes.

Examples

			75557 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

• Patrick De Geest, PDP Reference Table - 757.
• Makoto Kamada, Prime numbers of the form 755...557.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A082713.

Programs

Mathematica

Select[Range[0, 2000], PrimeQ[(680 10^# + 13) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)

PARI

a=77;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a-13)

PARI

for(n=0,1000,if(isprime((680*10^n+13)/9),print1(n,",")))

Formula

a(n) = A082713(n) - 2.

Extensions

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

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 05 2007

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

Three more terms added from Table, a link added, and comments section updated by Patrick De Geest, Nov 02 2014

Edited by Ray Chandler, Nov 05 2014