A101136 Indices of primes in sequence defined by A(0) = 79, A(n) = 10*A(n-1) - 61 for n > 0.

0, 2, 3, 6, 8, 12, 32, 36, 75, 146, 296, 1850, 3456, 3608, 45218

Offset

1,2

Comments

Numbers n such that (650*10^n + 61)/9 is prime.

Numbers n such that digit 7 followed by n >= 0 occurrences of digit 2 followed by digit 9 is prime.

Numbers corresponding to terms <= 296 are certified primes.

a(16) > 10^5. - Robert Price, Oct 01 2015

All a(n) == 0, 2 or 3 mod 6 (cf. A047244). - Robert Israel, Oct 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..15.

Makoto Kamada, Prime numbers of the form 722...229.

Index entries for primes involving repunits.

Formula

a(n) = A103054(n) - 1.

Example

72222229 is prime, hence 6 is a term.

Maple

select(t -> isprime((650*10^t + 61)/9), [seq(seq(6*s+i, i=[0, 2, 3]), s=0..700)]); # Robert Israel, Oct 01 2015

Mathematica

Select[Range[0, 100000], PrimeQ[(650*10^# + 61)/9] &] (* Robert Price, Oct 01 2015 *)

Prog

(PARI) a=79; for(n=0, 1000, if(isprime(a), print1(n, ", ")); a=10*a-61)
(PARI) for(n=0, 1000, if(isprime((650*10^n+61)/9), print1(n, ", ")))
(Magma) [n: n in [0..3*10^2]| IsPrime((650*10^n+61) div 9)]; // Vincenzo Librandi, Oct 02 2015

Crossrefs

Cf. A000533, A002275, A103054.

Sequence in context: A058298 A299758 A303703 * A036957 A319390 A251260

Adjacent sequences: A101133 A101134 A101135 * A101137 A101138 A101139

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(15) from Erik Branger May 01 2013 by Ray Chandler, Apr 30 2015

Status

approved