A101129 Indices of primes in sequence defined by A(0) = 73, A(n) = 10*A(n-1) - 27 for n > 0.

0, 3, 5, 15, 21, 38, 102, 162, 239, 1047, 1973, 2558, 5879, 14435, 28337, 32795, 38078, 56778, 91214, 111324, 115862, 138603

Offset: 1

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 03 2004

Keywords

• nonn
• hard
• more

Comments

Numbers n such that 70*10^n + 3 is prime.

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

Numbers corresponding to terms <= 239 are certified primes.

Certified primality of number corresponding to term 1047 with Primo. - Ryan Propper, Jun 20 2005

a(23) > 2*10^5. - Robert Price, Aug 15 2015

Examples

			7000003 is prime, hence 5 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 700...003.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A097970.

Programs

Magma

[n: n in [0..500] | IsPrime(70*10^n + 3)]; // Vincenzo Librandi, Aug 16 2015

Mathematica

Select[Range[0, 200000], PrimeQ[70*10^# + 3] &] (* Robert Price, Aug 15 2015 *)

PARI

a=73;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-27)

PARI

for(n=0,1500,if(isprime(70*10^n+3),print1(n,",")))

Formula

a(n) = A097970(n) - 1.

Extensions

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(14)-a(19) from Kamada data by Ray Chandler, Apr 29 2015

a(20)-a(22) from Robert Price, Aug 15 2015