A101951 Indices of primes in sequence defined by A(0) = 23, A(n) = 10*A(n-1) - 27 for n > 0.

0, 2, 4, 5, 6, 11, 15, 16, 21, 23, 34, 114, 119, 357, 1487, 1818, 4678, 9820, 27216, 27692, 194412

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 20*10^n + 3 is prime.

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

Numbers corresponding to terms <= 357 are certified primes.

a(21) > 10^5. - Robert Price, Nov 16 2014

a(22) > 2*10^5. - Robert Price, Jul 11 2015

Examples

			2003 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 200...003.

Crossrefs

Cf. A000533, A002275, A081677.

Programs

Magma

[n: n in [0..500] | IsPrime(20*10^n+3)]; // Vincenzo Librandi, Nov 17 2014

Mathematica

Select[Range[0, 1000], PrimeQ[(20 10^# + 3)] &] (* Vincenzo Librandi, Nov 17 2014 *)

PARI

a=23;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-27)

PARI

for(n=0,1500,if(isprime(20*10^n+3),print1(n,",")))

Formula

a(n) = A081677(n+1) - 1. - Robert Price, Nov 16 2014

Extensions

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

a(19)-a(20) derived from A081677 by Robert Price, Nov 16 2014

a(21) from Robert Price, Jul 11 2015