A101849 Indices of primes in sequence defined by A(0) = 37, A(n) = 10*A(n-1) + 27 for n > 0.

0, 1, 13, 19, 29, 43, 65, 259, 871, 8845, 26743, 57505, 98471, 106891

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 - 27)/9 is prime.

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

Numbers corresponding to terms <= 871 are certified primes.

a(14) > 10^5. - Robert Price, Mar 17 2015.

a(15) > 2*10^5. - Robert Price, Oct 02 2015

Examples

			397 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 399...997.
• Index entries for primes involving repunits.

Crossrefs

Cf. A000533, A002275, A101155, A169830, A101398.

Programs

Mathematica

Select[Range[0, 1000], PrimeQ[(360*10^# - 27)/9] &] (* Robert Price, Mar 17 2015 *)

PARI

a=37;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+27)

PARI

for(n=0,1500,if(isprime((360*10^n-27)/9),print1(n,",")))

Formula

a(n) = A101398(n) - 1.

Extensions

8845 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

a(11)-a(13) derived from A101398 by Robert Price, Mar 17 2015

a(14) from Robert Price, Oct 02 2015