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 A056245 Indices of primes in sequence defined by A(0) = 11, A(n) = 10*A(n-1) + 31 for n > 0. 1
 0, 5, 65, 1253, 8405, 67037 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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 REFERENCES Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467. LINKS Patrick De Geest, PDP Reference Table - 141. Makoto Kamada, Prime numbers of the form 144...441. FORMULA a(n) = A082698(n-1) - 2 for n > 1. EXAMPLE 1444441 is prime, hence 5 is a term. MATHEMATICA Select[Range[0, 2000], PrimeQ[(130 10^# - 31) / 9] &] (* Vincenzo Librandi, Nov 03 2014 PROG (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 CROSSREFS Cf. A000533, A002275, A082698. Sequence in context: A234871 A349517 A121822 * A357338 A195886 A079482 Adjacent sequences: A056242 A056243 A056244 * A056246 A056247 A056248 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), 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 STATUS approved

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Last modified March 29 17:39 EDT 2023. Contains 361599 sequences. (Running on oeis4.)