A101079 - OEIS

%I #21 Sep 08 2022 08:45:15

%S 0,5,8,9,11,12,22,60,193,232,548,764,972,1060,1185,1852,3712,6788,

%T 7253,7764,9024,10854,23639,31439,31838,32286,120341,132147

%N Indices of primes in sequence defined by A(0) = 83, A(n) = 10*A(n-1) + 63 for n > 0.

%C Numbers n such that (810*10^n - 63)/9 is prime.

%C Numbers n such that digit 8 followed by n >= 0 occurrences of digit 9 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 972 are certified primes.

%C a(29) > 2*10^5. - _Robert Price_, Sep 04 2015

%D Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

%H Makoto Kamada, <a href="https://stdkmd.net/nrr/8/89993.htm#prime">Prime numbers of the form 899...993</a>.

%H <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.

%F a(n) = A103092(n+1) - 1.

%e 8999993 is prime, hence 5 is a term.

%t Flatten[Position[Table[FromDigits[Join[{8},PadRight[{},n,9],{3}]],{n,0,1200}],_?PrimeQ]]-1 (* _Harvey P. Dale_, Mar 16 2013 *)

%o (PARI) a=83;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+63)

%o (PARI) for(n=0,1500,if(isprime((810*10^n-63)/9),print1(n,",")))

%o (Magma) [n: n in [0..400] | IsPrime(((810*10^n-63) div 9))]; // _Vincenzo Librandi_, Sep 05 2015

%Y Cf. A000533, A002275, A103092.

%K nonn,hard,more

%O 1,2

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Nov 30 2004

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

%E a(23)-a(26) from Kamada data by _Ray Chandler_, Apr 29 2015

%E a(27)-a(28) from _Robert Price_, Sep 04 2015