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A056245
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Indices of primes in sequence defined by A(0) = 11, A(n) = 10*A(n-1) + 31 for n > 0.
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1
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OFFSET
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1,2
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COMMENTS
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Numbers n such that (130*10^n - 31)/9 is prime.
Numbers n such that digit 1 followed by n >= 0 occurrences of digit 4 followed by digit 1 is prime.
Numbers corresponding to terms <= 1253 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.
a(7) > 2*10^5. - Tyler Busby, Feb 01 2023
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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..6.
Patrick De Geest, PDP Reference Table - 141.
Makoto Kamada, Prime numbers of the form 144...441.
Index entries for primes involving repunits.
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FORMULA
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a(n) = A082698(n-1) - 2 for n > 1.
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EXAMPLE
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1444441 is prime, hence 5 is a term.
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MATHEMATICA
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Select[Range[0, 2000], PrimeQ[(130 10^# - 31) / 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+31)
(PARI) for(n=0, 1500, if(isprime((130*10^n-31)/9), print1(n, ", ")))
(Magma) [n: n in [0..500] | IsPrime((130*10^n-31) div 9)]; // Vincenzo Librandi, Nov 03 2014
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CROSSREFS
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Cf. A000533, A002275, A082698.
Sequence in context: A234871 A349517 A121822 * A357338 A195886 A079482
Adjacent sequences: A056242 A056243 A056244 * A056246 A056247 A056248
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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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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
8405 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
Added one more term from the PDP table and updated 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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