A101973 Indices of primes in sequence defined by A(0) = 23, A(n) = 10*A(n-1) + 63 for n > 0.

0, 1, 4, 9, 28, 38, 113, 483, 864, 4179, 5384, 13121, 13831, 22675, 25019, 30056, 35909, 37934, 42294, 50193, 110075, 184123, 191151

Offset: 1

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 23 2004

Keywords

• nonn
• hard
• more

Comments

Numbers n such that (270*10^n - 63)/9 is prime.

Numbers n such that digit 2 followed by n >= 0 occurrences of digit 9 followed by digit 3 is prime.

Numbers corresponding to terms <= 864 are certified primes.

a(21) > 10^5. - Robert Price, Jan 25 2015

a(24) > 2*10^5. - Robert Price, Aug 09 2015

Examples

			293 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 299...993.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A102964.

Programs

Mathematica

Select[Range[0, 200000], PrimeQ[(270*10^# - 63)/9] &] (* Robert Price, Aug 09 2015 *)

PARI

a=23;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+63)

PARI

for(n=0,1500,if(isprime((270*10^n-63)/9),print1(n,",")))

Formula

a(n) = A102964(n) - 1.

Extensions

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

a(12)-a(20) derived from A102964 by Robert Price, Jan 25 2015

a(21)-a(23) derived from A102964 by Robert Price, Aug 09 2015