A101824 Indices of primes in sequence defined by A(0) = 37, A(n) = 10*A(n-1) - 63 for n > 0.

0, 1, 4, 7, 23, 28, 83, 109, 128, 175, 592, 1136, 2674, 4991, 26903, 31571, 55076, 81020, 122273

Offset: 1

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 20 2004

Keywords

• nonn
• hard
• more

Comments

Numbers n such that 30*10^n + 7 is prime.

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

Certified primality of term 1136 using Primo. - Ryan Propper, Jun 18 2005

a(19) > 10^5. - Robert Price, Jan 26 2015

a(20) > 2*10^5. - Robert Price, Jul 04 2015

Examples

			307 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 300...007.

Crossrefs

Cf. A000533, A002275, A100501.

Programs

PARI

a=37;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-63)

PARI

for(n=0,1500,if(isprime(30*10^n+7),print1(n,",")))

Formula

a(n) = A100501(n) - 1.

Extensions

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

a(16)-a(18) derived from A100501 by Robert Price, Jan 26 2015

a(19) from Robert Price, Jul 04 2015