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A056266
Indices of primes in sequence defined by A(0) = 99, A(n) = 10*A(n-1) - 1 for n > 0.
2
5, 71, 95, 113, 203, 983, 1225, 4793, 20719, 133579, 411589
OFFSET
1,1
COMMENTS
Numbers n such that (890*10^n + 1)/9 is prime.
Numbers n such that the number 9 8(n times) 9 is prime.
Numbers corresponding to terms <= 983 are certified primes. For numbers greater than 4793, see P. De Geest, PDP Reference Table.
REFERENCES
Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.
FORMULA
a(n) = A082719(n) - 2.
EXAMPLE
9888889 is prime, hence 5 is a term.
MATHEMATICA
Select[Range[2000], PrimeQ[(890 10^# + 1) / 9] &] (* Vincenzo Librandi, Nov 02 2014 *)
PROG
(PARI) a=99; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a-1)
(PARI) for(n=0, 1500, if(isprime((890*10^n+1)/9), print1(n, ", ")))
(Magma) [n: n in [0..1000] | IsPrime((890*10^n+1) div 9)]; // Vincenzo Librandi, Nov 02 2014
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Robert G. Wilson v, Aug 18 2000
EXTENSIONS
Additional comments from Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004
Edited by N. J. A. Sloane, Apr 17 2007
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
Two more terms from PDP table added and comments section edited by Patrick De Geest, Nov 02 2014
Edited by Ray Chandler, Nov 05 2014
STATUS
approved