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

1,1

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.

References

Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Links

Table of n, a(n) for n=1..5.

Patrick De Geest, PDP Reference Table - 343.

Makoto Kamada, Prime numbers of the form 344...443.

Index entries for primes involving repunits.

Formula

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

Example

3444443 is prime, hence 5 is a term.

Mathematica

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

Prog

(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, ", ")))

Crossrefs

Cf. A000533, A002275, A082706.

Sequence in context: A228054 A283354 A156330 * A101832 A046957 A174957

Adjacent sequences: A056250 A056251 A056252 * A056254 A056255 A056256

Keyword

nonn,hard,more

Author

Robert G. Wilson v, Aug 18 2000

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

Status

approved