login
A056253
Indices of primes in sequence defined by A(0) = 33, A(n) = 10*A(n-1) + 13 for n > 0.
2
5, 11, 491, 5567, 24755
OFFSET
1,1
COMMENTS
Numbers n such that (310*10^n - 13)/9 is prime.
Numbers n such that digit 3 followed by n >= 0 occurrences of digit 4 followed by digit 3 is prime.
Numbers corresponding to terms <= 491 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.
a(4) = 5567 is based on A082706.
REFERENCES
Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.
FORMULA
a(n) = A082706(n) - 2.
EXAMPLE
3444443 is prime, hence 5 is a term.
MATHEMATICA
Select[Range[0, 2000], PrimeQ[(310 10^# -13) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)
PROG
(PARI) a=33; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+13)
(PARI) for(n=0, 1500, if(isprime((310*10^n-13)/9), print1(n, ", ")))
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Robert G. Wilson v, Aug 18 2000
EXTENSIONS
24755 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
Comments section and a link edited by Patrick De Geest, Nov 02 2014
Edited by Ray Chandler, Nov 05 2014
STATUS
approved