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A101079
Indices of primes in sequence defined by A(0) = 83, A(n) = 10*A(n-1) + 63 for n > 0.
1
0, 5, 8, 9, 11, 12, 22, 60, 193, 232, 548, 764, 972, 1060, 1185, 1852, 3712, 6788, 7253, 7764, 9024, 10854, 23639, 31439, 31838, 32286, 120341, 132147
OFFSET
1,2
COMMENTS
Numbers n such that (810*10^n - 63)/9 is prime.
Numbers n such that digit 8 followed by n >= 0 occurrences of digit 9 followed by digit 3 is prime.
Numbers corresponding to terms <= 972 are certified primes.
a(29) > 2*10^5. - Robert Price, Sep 04 2015
REFERENCES
Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.
FORMULA
a(n) = A103092(n+1) - 1.
EXAMPLE
8999993 is prime, hence 5 is a term.
MATHEMATICA
Flatten[Position[Table[FromDigits[Join[{8}, PadRight[{}, n, 9], {3}]], {n, 0, 1200}], _?PrimeQ]]-1 (* Harvey P. Dale, Mar 16 2013 *)
PROG
(PARI) a=83; for(n=0, 1500, if(isprime(a), print1(n, ", ")); a=10*a+63)
(PARI) for(n=0, 1500, if(isprime((810*10^n-63)/9), print1(n, ", ")))
(Magma) [n: n in [0..400] | IsPrime(((810*10^n-63) div 9))]; // Vincenzo Librandi, Sep 05 2015
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 30 2004
EXTENSIONS
More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008
a(23)-a(26) from Kamada data by Ray Chandler, Apr 29 2015
a(27)-a(28) from Robert Price, Sep 04 2015
STATUS
approved