A101714 Indices of primes in sequence defined by A(0) = 47, A(n) = 10*A(n-1) - 63 for n > 0.

0, 2, 8, 38, 2322

Offset: 1

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 14 2004

Keywords

• nonn
• hard
• more

Comments

Numbers n such that 40*10^n + 7 is prime.

Numbers n such that digit 4 followed by n >= 0 occurrences of digit 0 followed by digit 7 is prime.

Some of the larger entries may only correspond to probable primes.

a(6) > 2*10^5. - Robert Price May 16 2015

Examples

			4007 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 400...007.

Crossrefs

Cf. A000533, A002275, A101395.

Programs

Mathematica

Select[Range[0, 3000], PrimeQ[40*10^# + 7] &] (* Robert Price, May 16 2015 *)

PARI

a=47;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-63)

PARI

for(n=0,1500,if(isprime(40*10^n+7),print1(n,",")))

Formula

a(n) = A101395(n+1) - 1.