A101727 Indices of primes in sequence defined by A(0) = 47, A(n) = 10*A(n-1) - 13 for n > 0.

0, 1, 3, 4, 12, 21, 24, 27, 37, 66, 141, 283, 294, 379, 396, 1216, 1639, 2884, 3285, 7734, 29305

Offset: 1

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 14 2004

Keywords

• nonn
• hard
• more

Comments

Numbers n such that (410*10^n + 13)/9 is prime.

Numbers n such that digit 4 followed by n >= 0 occurrences of digit 5 followed by digit 7 is prime.

Numbers corresponding to terms <= 396 are certified primes.

a(22) > 10^5. - Robert Price, May 22 2015

Examples

			457 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

• Makoto Kamada, Prime numbers of the form 455...557.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A102992.

Programs

Mathematica

Select[Range[0, 1000], PrimeQ[(410*10^# + 13)/9] &] (* Robert Price, May 22 2015 *)

PARI

a=47;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-13)

PARI

for(n=0,1500,if(isprime((410*10^n+13)/9),print1(n,",")))

Formula

a(n) = A102992(n) - 1.

Extensions

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

a(21) from Kamada data by Ray Chandler, Apr 30 2015