A101833 - OEIS

%I #14 Jan 17 2019 13:44:06

%S 0,1,757,1333,2176,4438,5197,6682,35989,47134

%N Indices of primes in sequence defined by A(0) = 37, A(n) = 10*A(n-1) - 23 for n > 0.

%C Numbers n such that (310*10^n + 23)/9 is prime.

%C Numbers n such that digit 3 followed by n >= 0 occurrences of digit 4 followed by digit 7 is prime.

%C Numbers corresponding to terms <= 757 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/3/34447.htm#prime">Prime numbers of the form 344...447</a>.

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

%F a(n) = A102969(n) - 1.

%e 347 is prime, hence 1 is a term.

%t For[n=0, n <= 4000, n++, If[PrimeQ[(310*10^n + 23)/9], Print[n]]] (Steinerberger)

%o (PARI) a=37;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-23)

%o (PARI) for(n=0,1500,if(isprime((310*10^n+23)/9),print1(n,",")))

%Y Cf. A000533, A002275, A102969.

%K nonn,hard

%O 1,3

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

%E a(5) from _Stefan Steinerberger_, Feb 04 2006

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

%E a(9)-a(10) from Kamada data by _Ray Chandler_, May 01 2015