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

Author

Robert G. Wilson v, Aug 18 2000

Keywords

• nonn
• hard
• more

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.

Examples

			3222223 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 - 323.
• Makoto Kamada, Prime numbers of the form 322...223.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A082705.

Programs

Mathematica

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

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,",")))

Formula

a(n) = A082705(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, 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