A102007 Indices of primes in sequence defined by A(0) = 17, A(n) = 10*A(n-1) - 63 for n > 0.

0, 1, 3, 7, 8, 23, 59, 109, 133, 221, 411, 699, 998, 1382, 5075, 5542, 6343, 14599, 15092, 21716, 23635, 30220, 50710, 221627, 350070, 371695, 487290, 995255

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 + 7 is prime.

Numbers n such that digit 1 followed by n >= 0 occurrences of digit 0 followed by digit 7 is prime.

Numbers corresponding to terms <= 998 are certified primes.

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

Examples

			10007 is prime, hence 3 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...007.

Crossrefs

Cf. A000533, A002275, A088274.

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[10*10^# + 7] &] (* Robert Price, Nov 09 2015 *)

PARI

a=17;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-63)

PARI

for(n=0,1500,if(isprime(10*10^n+7),print1(n,",")))

Formula

a(n) = A088274(n) - 1.

Extensions

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

a(24)-a(28) added from A088274 by Amiram Eldar, Nov 28 2021