A101138 Indices of primes in sequence defined by A(0) = 79, A(n) = 10*A(n-1) - 51 for n > 0.

0, 1, 4, 6, 84, 344, 1594, 2104, 6385, 9118, 9331, 14706, 72559

Offset

1,3

Comments

Numbers n such that (660*10^n + 51)/9 is prime.

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

Numbers corresponding to terms <= 344 are certified primes.

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..13.

Makoto Kamada, Prime numbers of the form 733...339.

Index entries for primes involving repunits.

Formula

a(n) = A103056(n+1) - 1.

Example

733339 is prime, hence 4 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(660*10^# + 51)/9] &] (* Robert Price, Sep 26 2015 *)

Prog

(PARI) a=79; for(n=0, 1000, if(isprime(a), print1(n, ", ")); a=10*a-51)
(PARI) for(n=0, 1000, if(isprime((660*10^n+51)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103056.

Sequence in context: A012970 A196814 A213335 * A222483 A245011 A375671

Adjacent sequences: A101135 A101136 A101137 * A101139 A101140 A101141

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 03 2004

Extensions

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

a(12) from Kamada data by Ray Chandler, Apr 30 2015

a(13) from Robert Price, Sep 26 2015

Status

approved