A101956 - OEIS

%I #19 Jan 17 2019 13:44:06

%S 0,1,2,3,7,10,12,23,27,51,53,93,296,656,1005,5346,8188,9313,23054,

%T 53286,64806

%N Indices of primes in sequence defined by A(0) = 29, A(n) = 10*A(n-1) - 51 for n > 0.

%C Numbers n such that (210*10^n + 51)/9 is prime.

%C Numbers n such that digit 2 followed by n >= 0 occurrences of digit 3 followed by digit 9 is prime.

%C Numbers corresponding to terms <= 656 are certified primes.

%C a(22) > 10^5. - _Robert Price_, Nov 25 2014

%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/2/23339.htm#prime">Prime numbers of the form 233...339</a>.

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

%F a(n) = A102951(n) - 1. - _Robert Price_, Nov 25 2014

%e 2339 is prime, hence 2 is a term.

%t Transpose[Select[Partition[With[{no=10000},Riffle[NestList[10#-51&,29,no],Range[0,no]]],2],PrimeQ[First[#]]&]][[2]]  (* _Harvey P. Dale_, Feb 05 2011 *)

%o (PARI) a=29;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-51)

%o (PARI) for(n=0,1500,if(isprime((210*10^n+51)/9),print1(n,",")))

%Y Cf. A000533, A002275, A102951.

%K nonn,hard,more

%O 1,3

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 23 2004

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

%E a(19)-a(21) derived from A102951 by _Robert Price_, Nov 25 2014