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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
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.
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
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