A101731 Indices of primes in sequence defined by A(0) = 47, A(n) = 10*A(n-1) - 3 for n > 0.

0, 1, 5, 9, 11, 12, 21, 31, 45, 60, 67, 89, 109, 651, 1607, 1903, 2002, 3037, 3085, 9579, 9697, 10638, 14460

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 + 3)/9 is prime.

Numbers n such that digit 4 followed by n >= 0 occurrences of digit 6 followed by digit 7 is prime.

Numbers corresponding to terms <= 651 are certified primes.

a(24) > 2*10^5. - Robert Price, Jul 11 2015

Examples

			467 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...667.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A099017.

Programs

Magma

[n: n in [0..500] | IsPrime((420*10^n+3) div 9)]; // Vincenzo Librandi, Jul 12 2015

Mathematica

Select[Range[0, 100], PrimeQ[(420 10^# + 3)/9] &] (* Vincenzo Librandi, Jul 12 2015 *)

PARI

a=47;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-3)

PARI

for(n=0,1500,if(isprime((420*10^n+3)/9),print1(n,",")))

Formula

a(n) = A099017(n+1) - 1.

Extensions

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

a(22)-a(23) from Kamada data by Ray Chandler, Apr 30 2015