A056254 Indices of primes in sequence defined by A(0) = 33, A(n) = 10*A(n-1) + 23 for n > 0.

1, 7, 139, 229, 425, 461, 725, 1973, 7229, 45859, 47303

Offset

1,2

Comments

Numbers n such that (320*10^n - 23)/9 is prime.

Numbers n such that digit 3 followed by n >= 0 occurrences of digit 5 followed by digit 3 is prime.

Numbers corresponding to terms <= 1973 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.

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..11.

Patrick De Geest, PDP Reference Table - 353.

Makoto Kamada, Prime numbers of the form 355...553.

Index entries for primes involving repunits.

Formula

a(n) = A082707(n) - 2.

Example

353 is prime, hence 1 is a term.

Mathematica

Select[Range[0, 2000], PrimeQ[(320 10^# - 23) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)

Prog

(PARI) a=33; for(n=0, 2000, if(isprime(a), print1(n, ", ")); a=10*a+23)
(PARI) for(n=0, 2000, if(isprime((320*10^n-23)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A082707.

Sequence in context: A171106 A217504 A142295 * A137463 A274525 A221375

Adjacent sequences: A056251 A056252 A056253 * A056255 A056256 A056257

Keyword

nonn,hard

Author

Robert G. Wilson v, Aug 18 2000

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, May 31 2007, Jun 15 2007

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

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

Edited by Ray Chandler, Nov 05 2014

Status

approved