A101848 Indices of primes in sequence defined by A(0) = 31, A(n) = 10*A(n-1) + 81 for n > 0.

0, 16, 18, 28, 42, 118, 172, 948, 1608, 5578, 19678, 34146, 43492, 97798

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 (360*10^n - 81)/9 is prime.

Numbers n such that digit 3 followed by n >= 0 occurrences of digit 9 followed by digit 1 is prime.

Numbers corresponding to terms <= 948 are certified primes.

a(15) > 10^5. - Robert Price, Mar 17 2015

Examples

			31 is prime, hence 0 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 399...991.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A101396.

Programs

Mathematica

Select[Range[0, 1000], PrimeQ[(360*10^# - 81)/9] &] (* Robert Price, Mar 17 2015 *)

PARI

a=31;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+81)

PARI

for(n=0,1500,if(isprime((360*10^n-81)/9),print1(n,",")))

Formula

a(n) = A101396(n) - 1.

Extensions

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

a(12)-a(14) derived from A101396 by Robert Price, Mar 17 2015