A056245 Indices of primes in sequence defined by A(0) = 11, A(n) = 10*A(n-1) + 31 for n > 0.

0, 5, 65, 1253, 8405, 67037

Offset: 1

Author

Robert G. Wilson v, Aug 18 2000

Keywords

• nonn
• hard
• more

Comments

Numbers n such that (130*10^n - 31)/9 is prime.

Numbers n such that digit 1 followed by n >= 0 occurrences of digit 4 followed by digit 1 is prime.

Numbers corresponding to terms <= 1253 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.

a(7) > 2*10^5. - Tyler Busby, Feb 01 2023

Examples

			1444441 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 - 141.
• Makoto Kamada, Prime numbers of the form 144...441.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A082698.

Programs

Magma

[n: n in [0..500] | IsPrime((130*10^n-31) div 9)]; // Vincenzo Librandi, Nov 03 2014

Mathematica

Select[Range[0, 2000], PrimeQ[(130 10^# - 31) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)

PARI

a=11;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+31)

PARI

for(n=0,1500,if(isprime((130*10^n-31)/9),print1(n,",")))

Formula

a(n) = A082698(n-1) - 2 for n > 1.

Extensions

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

8405 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

Added one more term from the PDP table and updated a link, by Patrick De Geest, Nov 02 2014

Edited by Ray Chandler, Nov 04 2014