A101527 - OEIS

%I #18 Jan 17 2019 13:44:06

%S 0,1,6,18,24,36,48,132,612,1339,2035,2490,26262

%N Indices of primes in sequence defined by A(0) = 61, A(n) = 10*A(n-1) + 31 for n > 0.

%C Numbers n such that (580*10^n - 31)/9 is prime.

%C Numbers n such that digit 6 followed by n >= 0 occurrences of digit 4 followed by digit 1 is prime.

%C Numbers corresponding to terms <= 612 are certified primes.

%C a(14) > 10^5. - _Robert Price_, Sep 10 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/6/64441.htm#prime">Prime numbers of the form 644...441</a>.

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

%F a(n) = A103034(n+1) - 1.

%e 641 is prime, hence 1 is a term.

%t Select[Range[0, 100000], PrimeQ[(580*10^# - 31)/9] &] (* _Robert Price_, Sep 10 2015 *)

%o (PARI) a=61;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+31)

%o (PARI) for(n=0,1500,if(isprime((580*10^n-31)/9),print1(n,",")))

%Y Cf. A000533, A002275, A103034.

%K nonn,hard,more

%O 1,3

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 06 2004

%E Two more terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Dec 22 2007

%E a(13) from _Max Alekseyev_, Dec 12 2011