A102006 Indices of primes in sequence defined by A(0) = 13, A(n) = 10*A(n-1) - 27 for n > 0.

0, 1, 4, 5, 10, 16, 17, 38, 55, 100, 104, 106, 122, 412, 425, 2606, 7667, 10469, 11020, 17752, 26926, 60775, 98287, 300475

Offset: 1

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004

Keywords

• nonn
• hard
• more

Comments

Numbers n such that 10*10^n + 3 is prime.

Numbers n such that digit 1 followed by n >= 0 occurrences of digit 0 followed by digit 3 is prime.

Numbers corresponding to terms <= 425 are certified primes.

No other terms <99,999.

Examples

			100003 is prime, hence 4 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 100...003.

Crossrefs

Cf. A000533, A002275, A049054, A159352.

Programs

PARI

a=13;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-27)

PARI

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

Formula

a(n) = A049054(n) - 1.

Extensions

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

a(22)=60775, a(23)=98287 from Robert Price, Mar 03 2011

a(24) from A049054 by Ray Chandler, May 01 2015