A101069 Indices of primes in sequence defined by A(0) = 89, A(n) = 10*A(n-1) - 41 for n > 0.

0, 3, 12, 36, 45, 105, 138, 468, 5694, 56280, 58669

Offset

1,2

Comments

Numbers n such that (760*10^n + 41)/9 is prime.

Numbers n such that digit 8 followed by n >= 0 occurrences of digit 4 followed by digit 9 is prime.

Numbers corresponding to terms <= 468 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..11.

Makoto Kamada, Prime numbers of the form 844...449.

Index entries for primes involving repunits.

Formula

a(n) = A103082(n+1) - 1. - Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

Example

84449 is prime, hence 3 is a term.

Mathematica

Select[Range[0, 5700], PrimeQ[FromDigits[Join[PadRight[{8}, #+1, 4], {9}]]]&] (* Harvey P. Dale, Jan 23 2012 *)

Prog

(PARI) a=89; for(n=0, 1000, if(isprime(a), print1(n, ", ")); a=10*a-41)
(PARI) for(n=0, 1000, if(isprime((760*10^n+41)/9), print1(n, ", ")))

Crossrefs

Cf. A000533, A002275, A103082.

Sequence in context: A232899 A009787 A135190 * A225259 A334891 A242526

Adjacent sequences: A101066 A101067 A101068 * A101070 A101071 A101072

Keyword

nonn,hard,more

Author

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

Extensions

One more term from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

a(10)-a(11) from Robert Price, Oct 18 2015

Status

approved