A101729 Indices of primes in sequence defined by A(0) = 41, A(n) = 10*A(n-1) + 51 for n > 0.

0, 1, 6, 8, 13, 23, 44, 48, 72, 73, 231, 337, 396, 503, 1062, 2816, 5304, 16767, 27059

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 (420*10^n - 51)/9 is prime.

Numbers n such that digit 4 followed by n >= 0 occurrences of digit 6 followed by digit 1 is prime.

Numbers corresponding to terms <= 503 are certified primes.

a(20) > 10^5. - Robert Price, May 27 2015

Examples

			461 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 466...661.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A102994.

Programs

Mathematica

Select[Range[0, 1000], PrimeQ[(420*10^# - 51)/9] &] (* Robert Price, May 27 2015 *)

PARI

a=41;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+51)

PARI

for(n=0,1500,if(isprime((420*10^n-51)/9),print1(n,",")))

Formula

a(n) = A102994(n) - 1.

Extensions

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

a(18)-a(19) from Kamada data by Ray Chandler, Apr 30 2015