A101155 Indices of primes in sequence defined by A(0) = 73, A(n) = 10*A(n-1) + 63 for n > 0.

0, 2, 4, 5, 9, 11, 12, 38, 47, 53, 63, 81, 146, 147, 359, 398, 1637, 1875, 2145, 2193, 15788, 23073, 38465, 68399

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 (720*10^n - 63)/9 is prime.

Numbers n such that digit 7 followed by n >= 0 occurrences of digit 9 followed by digit 3 is prime.

Numbers corresponding to terms <= 398 are certified primes.

a(25) > 2*10^5. - Robert Price, Nov 11 2015

Examples

			7999993 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 799...993.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A101849, A169830, A099190.

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(720*10^# - 63)/9] &] (* Robert Price, Nov 11 2015 *)

PARI

a=73;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a+63)

PARI

for(n=0,1000,if(isprime((720*10^n-63)/9),print1(n,",")))

Formula

a(n) = A099190(n) - 1.

Extensions

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

a(21)-a(24) from Kamada data by Ray Chandler, Apr 30 2015