A101073 Indices of primes in sequence defined by A(0) = 89, A(n) = 10*A(n-1) - 31 for n > 0.

0, 1, 7, 16, 18, 24, 39, 48, 57, 58, 91, 112, 295, 636, 1855, 2514, 3592, 6990, 11839, 86071, 93507

Offset

1,3

Comments

Numbers n such that (770*10^n + 31)/9 is prime.

Numbers n such that digit 8 followed by n >= 0 occurrences of digit 5 followed by digit 9 is prime.

Numbers corresponding to terms <= 636 are certified primes.

a(22) > 10^5. - Robert Price, Oct 26 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..21.

Makoto Kamada, Prime numbers of the form 855...559.

Index entries for primes involving repunits.

Formula

a(n) = A103086(n) - 1.

Example

855555559 is prime, hence 7 is a term.

Mathematica

Flatten[Position[NestList[10#-31&, 89, 1000], _?PrimeQ]-1] (* As written, the program will generate the first 14 terms of the sequence; changing the constant from 1000 to 7000 will generate 18 terms of the sequence but it will take a long time to do so *) (* Harvey P. Dale, Jul 16 2012 *)
Select[Range[0, 100000], PrimeQ[(770*10^# + 31)/9] &] (* Robert Price, Oct 26 2015 *)

Prog

(PARI) a=89; for(n=0, 1000, if(isprime(a), print1(n, ", ")); a=10*a-31)
(PARI) for(n=0, 1000, if(isprime((770*10^n+31)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103086.

Sequence in context: A193688 A132348 A177763 * A026226 A335569 A349103

Adjacent sequences: A101070 A101071 A101072 * A101074 A101075 A101076

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

a(20)-a(21) from Robert Price, Oct 26 2015

Status

approved