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A056265
Indices of primes in sequence defined by A(0) = 99, A(n) = 10*A(n-1) - 61 for n > 0.
3
1, 5, 11, 109, 3607, 37783
OFFSET
1,2
COMMENTS
Numbers n such that (830*10^n + 61)/9 is prime. - Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004
Numbers n such that digit 9 followed by n >= 0 occurrences of digit 2 followed by digit 9 is prime.
Numbers corresponding to terms <= 3607 are certified primes. For number corresponding to 37783 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) = A082718(n) - 2.
EXAMPLE
9222229 is prime, hence 5 is a term.
MATHEMATICA
Do[If[PrimeQ[(9*10^n + 2*(10^n - 1)/9)*10 + 9], Print[n]], {n, 1, 2500}]
Select[Range[2000], PrimeQ[(830 10^# + 61) / 9] &] (* Vincenzo Librandi, Nov 02 2014 *)
PROG
(PARI) a=99; for(n=0, 1000, if(isprime(a), print1(n, ", ")); a=10*a-61) \\ Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004
(PARI) for(n=0, 1000, if(isprime((830*10^n + 61)/9), print1(n, ", "))) \\ Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004
(Magma) [n: n in [0..1000] | IsPrime((830*10^n + 61) div 9)]; // Vincenzo Librandi, Nov 02 2014
CROSSREFS
KEYWORD
hard,nonn,more
AUTHOR
Robert G. Wilson v, Aug 18 2000
EXTENSIONS
3607 from Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 27 2004
37783 from Patrick De Geest, Jun 26 2005
Edited by N. J. A. Sloane, Jan 14 2008
Edited by Ray Chandler, Oct 20 2010
Comments section edited by Patrick De Geest, Nov 02 2014
Editied by Ray Chandler, Nov 05 2014
STATUS
approved