A101057 Indices of primes in sequence defined by A(0) = 89, A(n) = 10*A(n-1) - 81 for n > 0.

0, 1, 2, 5, 11, 19, 20, 36, 41, 54, 59, 97, 99, 103, 222, 236, 259, 500, 569, 599, 697, 8856, 20910, 24344, 31963, 67741, 162923

Offset

1,3

Comments

Numbers n such that 80*10^n + 9 is prime.

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

Numbers corresponding to terms <= 697 are certified primes.

a(28) > 2*10^5. - Robert Price, Dec 18 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..27.

Makoto Kamada, Prime numbers of the form 800...009.

Index entries for primes involving repunits.

Formula

a(n) = A103070(n+1) - 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

Example

8000009 is prime, hence 5 is a term.

Mathematica

Do[If[PrimeQ[80*10^n + 9], Print[n]], {n, 0, 20000}] (* Robert Price, Dec 18 2015 *)

Prog

(PARI) a=89; for(n=0, 1000, if(isprime(a), print1(n, ", ")); a=10*a-81)
(PARI) for(n=0, 1000, if(isprime(80*10^n + 9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103070.

Sequence in context: A132455 A132459 A308517 * A045362 A157978 A282246

Adjacent sequences: A101054 A101055 A101056 * A101058 A101059 A101060

Keyword

nonn,hard,more

Author

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

Extensions

8856 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(23)-a(26) from Kamada data by Ray Chandler, Apr 29 2015

a(27) from Robert Price, Dec 18 2015

Status

approved