A056252 Indices of primes in sequence defined by A(0) = 33, A(n) = 10*A(n-1) - 7 for n > 0.

5, 7, 893, 1523, 3035, 21155

Offset

1,1

Comments

Numbers n such that (290*10^n + 7)/9 is prime.

Numbers n such that the digit 3 followed by n >= 0 occurrences of the digit 2 followed by the digit 3 is prime.

Numbers corresponding to terms <= 3035 are certified primes.

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..6.

Patrick De Geest, PDP Reference Table - 323.

Makoto Kamada, Prime numbers of the form 322...223.

Index entries for primes involving repunits.

Formula

a(n) = A082705(n) - 2.

Example

3222223 is prime, hence 5 is a term.

Mathematica

Select[Range[0, 2000], PrimeQ[(290 10^# + 7) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)

Prog

(PARI) a=33; for(n=0, 1600, if(isprime(a), print1(n, ", ")); a=10*a-7)
(PARI) for(n=0, 1600, if(isprime((290*10^n+7)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A082705.

Sequence in context: A114363 A083687 A101829 * A274774 A370190 A176599

Adjacent sequences: A056249 A056250 A056251 * A056253 A056254 A056255

Keyword

nonn,hard,more

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, Apr 17 2007

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

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

Edited by Ray Chandler, Nov 05 2014

Status

approved