A056244 Indices of primes in sequence defined by A(0) = 11, A(n) = 10*A(n-1) + 21 for n > 0.

0, 1, 3, 5, 93, 159, 359, 1469, 2897, 3093, 3111, 15697, 17955, 42261, 111031

Offset: 1

Author

Robert G. Wilson v, Aug 18 2000

Keywords

• nonn
• hard
• more

Comments

Numbers n such that (120*10^n - 21)/9 is prime.

Numbers n such that digit 1 followed by n >= 0 occurrences of digit 3 followed by digit 1 is prime.

Numbers corresponding to terms <= 3111 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.

Examples

			131 is prime, hence 1 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 - 131.
• Makoto Kamada, Prime numbers of the form 133...331.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A068645, A082697.

Programs

Mathematica

Do[If[PrimeQ[(1*10^n + 3*(10^n - 1)/9)*10 + 1], Print[n]], {n, 1, 2500}]
Select[Range[0, 2000], PrimeQ[(120 10^# - 21) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)

PARI

a=11;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+21)

PARI

for(n=0,1500,if(isprime((120*10^n-21)/9),print1(n,",")))

Formula

a(n) = A082697(n-1) - 2 for n > 1.

Extensions

More terms and additional comments from Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004

Edited by N. J. A. Sloane, Jun 15 2007

Updates from De Geest site by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(15)=111031 from Ray Chandler, Apr 14 2011

Updated comments section and a link, by Patrick De Geest, Nov 02 2014

Edited by Ray Chandler, Nov 04 2014