A101533 Indices of primes in sequence defined by A(0) = 67, A(n) = 10*A(n-1) - 13 for n > 0.

0, 3, 8, 20, 47, 83, 695, 1488, 4166, 8399, 52098

Offset

1,2

Comments

Numbers k such that (590*10^k + 13)/9 is prime.

Numbers k such that digit 6 followed by k >= 0 occurrences of digit 5 followed by digit 7 is prime.

Numbers corresponding to terms <= 695 are certified primes.

a(12) > 10^5. - Robert Price, Sep 20 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..11.

Makoto Kamada, Prime numbers of the form 655...557.

Index entries for primes involving repunits.

Formula

a(n) = A103040(n) - 1.

Example

65557 is prime, hence 3 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(590*10^# + 13)/9] &] (* Robert Price, Sep 20 2015 *)

Prog

(PARI) a=67; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-13)
(PARI) for(n=0, 1500, if(isprime((590*10^n+13)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103040.

Sequence in context: A026624 A026690 A036676 * A138803 A048492 A006776

Adjacent sequences: A101530 A101531 A101532 * A101534 A101535 A101536

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(11) from Robert Price, Sep 20 2015

Status

approved