A101071 Indices of primes in sequence defined by A(0) = 83, A(n) = 10*A(n-1) + 23 for n > 0.

0, 1, 6, 43, 55, 337, 1210, 2692, 3535, 3916, 3973, 4045, 6960, 23770, 69655

Offset

1,3

Comments

Numbers n such that (770*10^n - 23)/9 is a prime.

Numbers n such that digit 8 followed by n >= 0 occurrences of digit 5 followed by digit 3 is prime.

Numbers corresponding to terms <= 337 are certified primes.

a(16) > 10^5. - Robert Price, Oct 22 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 855...553.

Index entries for primes involving repunits.

Formula

a(n) = A103084(n) - 1.

Example

85555553 is prime, hence 6 is a term.

Mathematica

Select[Range[0, 100000], PrimeQ[(770*10^# - 23)/9] &] (* Robert Price, Oct 22 2015 *)

Prog

(PARI) a=83; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+23)
(PARI) for(n=0, 1500, if(isprime((770*10^n-23)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103084.

Sequence in context: A185222 A179861 A083940 * A299375 A097298 A012872

Adjacent sequences: A101068 A101069 A101070 * A101072 A101073 A101074

Keyword

nonn,hard,more

Author

Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 30 2004

Extensions

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

a(14) from Kamada data by Ray Chandler, Apr 29 2015

a(15) from Robert Price, Oct 22 2015

Status

approved