A101583 - OEIS

%I #22 Jan 17 2019 13:44:06

%S 0,1,2,9,24,28,33,72,75,76,650,883,937,1251,1892,3341,4033,6167,6215,

%T 6230,6811,11045,15447,16627,16917,18733,45934

%N Indices of primes in sequence defined by A(0) = 59, A(n) = 10*A(n-1) - 21 for n > 0.

%C Numbers n such that (510*10^n + 21)/9 is prime.

%C Numbers n such that digit 5 followed by n >= 0 occurrences of digit 6 followed by digit 9 is prime.

%C Numbers corresponding to terms <= 937 are certified primes.

%C a(28) > 10^5. - _Robert Price_, Sep 05 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/5/56669.htm#prime">Prime numbers of the form 566...669</a>.

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

%F a(n) = A103018(n) - 1.

%e 5669 is prime, hence 2 is a term.

%t Flatten[Position[NestList[10#-21&,59,940],_?PrimeQ]]-1 (* _Harvey P. Dale_, Aug 22 2012 *)

%o (PARI) a=59;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-21)

%o (PARI) for(n=0,1500,if(isprime((510*10^n+21)/9),print1(n,",")))

%Y Cf. A000533, A002275, A103018.

%K nonn,more

%O 1,3

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 09 2004

%E 7 additional terms, corresponding to probable primes, from _Ryan Propper_, Jun 24 2005. Next term after 6811 is greater than 10,000.

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

%E Edited by _T. D. Noe_, Oct 30 2008

%E a(27) from Erik Branger May 01 2013 by _Ray Chandler_, Apr 30 2015