A101733 Indices of primes in sequence defined by A(0) = 49, A(n) = 10*A(n-1) - 11 for n > 0.

1, 3, 25, 1270, 1411, 3327, 4675, 47050, 67663

Offset

1,2

Comments

Numbers n such that (430*10^n + 11)/9 is a prime.

Numbers n such that digit 4 followed by n >= 0 occurrences of digit 7 followed by digit 9 is a prime.

Some of the larger entries may only correspond to probable primes.

a(10) > 10^5. - Robert Price, Jun 01 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..9.

Makoto Kamada, Prime numbers of the form 477...779.

Index entries for primes involving repunits.

Formula

a(n) = A102996(n) - 1.

Example

47779 is a prime, hence 3 is a term.

Mathematica

Select[Range[0, 1000], PrimeQ[(430*10^# + 11)/9] &] (* Robert Price, Jun 01 2015 *)

Prog

(PARI) a=49; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-11)
(PARI) for(n=0, 1500, if(isprime((430*10^n+11)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A102996.

Sequence in context: A306792 A012764 A219275 * A309116 A094815 A246536

Adjacent sequences: A101730 A101731 A101732 * A101734 A101735 A101736

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 14 2004

Extensions

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

a(8) from Erik Branger May 01 2013 by Ray Chandler, May 01 2015

a(9) from Robert Price, Jun 01 2015

Status

approved