A101838 - OEIS

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

%S 1,2,4,7,13,76,194,217,956,1051,1162,1484,1730,1969,3236,17353,85963

%N Indices of primes in sequence defined by A(0) = 39, A(n) = 10*A(n-1) - 31 for n > 0.

%C Numbers n such that (320*10^n + 31)/9 is prime.

%C Numbers n such that digit 3 followed by n >= 0 occurrences of digit 5 followed by digit 9 is prime.

%C Numbers corresponding to terms <= 956 are certified primes.

%C a(18) > 10^5. - _Robert Price_, May 31 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/3/35559.htm#prime">Prime numbers of the form 355...559</a>.

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

%F a(n) = A102973(n+1) - 1.

%e 3559 is prime, hence 2 is a term.

%t For [n = 1, n <= 3000, n++, If[PrimeQ[(320*10^n + 31)/9], Print[n]]] (Steinerberger)

%o (PARI) a=39;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-31)

%o (PARI) for(n=0,1500,if(isprime((320*10^n+31)/9),print1(n,",")))

%Y Cf. A000533, A002275, A102973.

%K nonn,hard

%O 1,2

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 20 2004

%E a(9) and a(10) _Stefan Steinerberger_, Feb 03 2006

%E 3236 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

%E a(16) from Kamada data by _Ray Chandler_, May 01 2015

%E a(17) from _Robert Price_, May 31 2015