A101724 Indices of primes in sequence defined by A(0) = 47, A(n) = 10*A(n-1) - 33 for n > 0.

0, 2, 4, 5, 7, 14, 25, 52, 59, 96, 182, 204, 301, 395, 455, 466, 606, 827, 1859, 2742, 4272, 4780, 5711, 6037, 6636, 9221, 10831, 18864, 25847, 42246, 48546, 87564, 95587

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 (390*10^n + 33)/9 is prime.

Numbers n such that digit 4 followed by n >= 0 occurrences of digit 3 followed by digit 7 is prime.

Numbers corresponding to terms <= 827 are certified primes.

a(34) > 10^5. - Robert Price, May 11 2015

Examples

			4337 is prime, hence 2 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 433...337.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A102989.

Programs

Mathematica

Select[Range[0, 300], PrimeQ[(390*10^# + 33)/9] &] (* Robert Price, May 11 2015 *)

PARI

a=47;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-33)

PARI

for(n=0,1500,if(isprime((390*10^n+33)/9),print1(n,",")))

Formula

a(n) = A102989(n) - 1.

Extensions

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

a(27)-a(31) from Kamada data by Ray Chandler, Apr 30 2015

a(32)-a(33) from Robert Price, May 11 2015