A101531 - OEIS

%I #15 Jan 17 2019 13:44:06

%S 0,2,3,9,21,39,53,80,83,105,192,596,680,1362,1875,4023,14162,18732,

%T 20841,23727,26418,31449,44693,64766

%N Indices of primes in sequence defined by A(0) = 61, A(n) = 10*A(n-1) + 41 for n > 0.

%C Numbers n such that (590*10^n - 41)/9 is prime.

%C Numbers n such that digit 6 followed by n >= 0 occurrences of digit 5 followed by digit 1 is prime.

%C Numbers corresponding to terms <= 680 are certified primes.

%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/6/65551.htm#prime">Prime numbers of the form 655...551</a>.

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

%F a(n) = A103038(n+1) - 1.

%e 65551 is prime, hence 3 is a term.

%t Select[Range[0, 100000], PrimeQ[(590*10^# - 41)/9] &] (* _Robert Price_, Sep 11 2015 *)

%o (PARI) a=61;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+41)

%o (PARI) for(n=0,1500,if(isprime((590*10^n-41)/9),print1(n,",")))

%Y Cf. A000533, A002275, A103038.

%K nonn,hard,more

%O 1,2

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

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

%E a(17)-a(23) from Kamada data by _Ray Chandler_, Apr 30 2015

%E a(24) from _Robert Price_, Sep 11 2015