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A056244
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Indices of primes in sequence defined by A(0) = 11, A(n) = 10*A(n-1) + 21 for n > 0.
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2
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0, 1, 3, 5, 93, 159, 359, 1469, 2897, 3093, 3111, 15697, 17955, 42261, 111031
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OFFSET
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1,3
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COMMENTS
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Numbers n such that (120*10^n - 21)/9 is prime.
Numbers n such that digit 1 followed by n >= 0 occurrences of digit 3 followed by digit 1 is prime.
Numbers corresponding to terms <= 3111 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.
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REFERENCES
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Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.
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LINKS
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Table of n, a(n) for n=1..15.
Patrick De Geest, PDP Reference Table - 131.
Makoto Kamada, Prime numbers of the form 133...331.
Index entries for primes involving repunits.
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FORMULA
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a(n) = A082697(n-1) - 2 for n > 1.
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EXAMPLE
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131 is prime, hence 1 is a term.
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MATHEMATICA
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Do[If[PrimeQ[(1*10^n + 3*(10^n - 1)/9)*10 + 1], Print[n]], {n, 1, 2500}]
Select[Range[0, 2000], PrimeQ[(120 10^# - 21) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)
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PROG
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(PARI) a=11; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+21)
(PARI) for(n=0, 1500, if(isprime((120*10^n-21)/9), print1(n, ", ")))
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CROSSREFS
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Cf. A000533, A002275, A068645, A082697.
Sequence in context: A271925 A236365 A057663 * A173487 A279310 A103081
Adjacent sequences: A056241 A056242 A056243 * A056245 A056246 A056247
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KEYWORD
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nonn,hard,more
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AUTHOR
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Robert G. Wilson v, Aug 18 2000
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EXTENSIONS
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More terms and additional comments from Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004
Edited by N. J. A. Sloane, Jun 15 2007
Updates from De Geest site by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
a(15)=111031 from Ray Chandler, Apr 14 2011
Updated comments section and a link, by Patrick De Geest, Nov 02 2014
Edited by Ray Chandler, Nov 04 2014
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STATUS
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approved
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