A056251 Indices of primes in sequence defined by A(0) = 33, A(n) = 10*A(n-1) - 17 for n > 0.

1, 11, 13, 29, 103, 125, 341, 599, 9823

Offset: 1

Author

Robert G. Wilson v, Aug 18 2000

Keywords

• nonn
• hard
• more

Comments

Numbers n such that (280*10^n + 17)/9 is prime.

Numbers n such that digit 3 followed by n >= 0 occurrences of digit 1 followed by digit 3 is prime.

Numbers corresponding to terms <= 599 are certified primes.

All terms are odd since 11 is the only palindromic prime with an even number of digits. - Chai Wah Wu, Nov 05 2019

a(10) > 2*10^5. - Tyler Busby, Feb 01 2023

Examples

			313 is prime, hence 1 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 - 313.
• Makoto Kamada, Prime numbers of the form 311...113.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A068650, A082704.

Programs

Mathematica

Flatten[Position[NestList[10#-17&,33,600],?PrimeQ]-1] (* This generates the first 8 terms of the sequence. Changing the last constant from 600 to 9825 will generate all 9 terms of the sequence but it will take a long time to do so. - _Harvey P. Dale, May 16 2012 *)
Select[Range[0, 2000], PrimeQ[(280 10^# + 17) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)

PARI

a=33;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-17)

PARI

for(n=0,1500,if(isprime((280*10^n+17)/9),print1(n,",")))

Formula

a(n) = A082704(n) - 2.

Extensions

Additional comments from Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 20 2004

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 15 2007

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

Added and updated the links section, by Patrick De Geest, Nov 02 2014

Edited by Ray Chandler, Nov 04 2014