A101542 Indices of primes in sequence defined by A(0) = 67, A(n) = 10*A(n-1) + 27 for n > 0.

0, 2, 3, 5, 9, 19, 50, 137, 189, 359, 377, 392, 1383, 1593, 2758, 2867, 5394, 7493, 10490, 11198, 12189, 33593, 38255, 89168, 165915

Offset

1,2

Comments

Numbers n such that (630*10^n - 27)/9 is prime.

Numbers n such that digit 6 followed by n >= 0 occurrences of digit 9 followed by digit 7 is prime.

Numbers corresponding to terms <= 392 are certified primes.

a(26) > 2*10^5. - Robert Price, Aug 17 2015

References

Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Links

Table of n, a(n) for n=1..25.

Makoto Kamada, Prime numbers of the form 699...997.

Index entries for primes involving repunits.

Formula

a(n) = A103049(n) - 1.

Example

6997 is prime, hence 2 is a term.

Mathematica

Select[Range[0, 200000], PrimeQ[(630*10^# - 27)/9] &] (* Robert Price, Aug 17 2015 *)

Prog

(PARI) a=67; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+27)
(PARI) for(n=0, 1500, if(isprime((630*10^n-27)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103049.

Sequence in context: A123389 A113984 A110542 * A101581 A365044 A349676

Adjacent sequences: A101539 A101540 A101541 * A101543 A101544 A101545

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 06 2004

Extensions

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

a(19)-a(24) from Kamada data by Ray Chandler, Apr 30 2015

a(25) from Robert Price, Aug 17 2015

Status

approved