A056253 Indices of primes in sequence defined by A(0) = 33, A(n) = 10*A(n-1) + 13 for n > 0.

5, 11, 491, 5567, 24755

Offset: 1

Author

Robert G. Wilson v, Aug 18 2000

Keywords

• nonn
• hard
• more

Comments

Numbers n such that (310*10^n - 13)/9 is prime.

Numbers n such that digit 3 followed by n >= 0 occurrences of digit 4 followed by digit 3 is prime.

Numbers corresponding to terms <= 491 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.

a(4) = 5567 is based on A082706.

Examples

			3444443 is prime, hence 5 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 - 343.
• Makoto Kamada, Prime numbers of the form 344...443.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A082706.

Programs

Mathematica

Select[Range[0, 2000], PrimeQ[(310 10^# -13) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)

PARI

a=33;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+13)

PARI

for(n=0,1500,if(isprime((310*10^n-13)/9),print1(n,",")))

Formula

a(n) = A082706(n) - 2.

Extensions

24755 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

Comments section and a link edited by Patrick De Geest, Nov 02 2014

Edited by Ray Chandler, Nov 05 2014