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A101953 Indices of primes in sequence defined by A(0) = 23, A(n) = 10*A(n-1) - 17 for n > 0. 1

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

%S 0,2,6,12,23,29,47,51,162,174,218,227,260,753,950,1343,1572,3293,3522,

%T 14160,70793

%N Indices of primes in sequence defined by A(0) = 23, A(n) = 10*A(n-1) - 17 for n > 0.

%C Numbers n such that (190*10^n + 17)/9 is prime.

%C Numbers n such that digit 2 followed by n >= 0 occurrences of digit 1 followed by digit 3 is prime.

%C Numbers corresponding to terms <= 950 are certified primes.

%C a(22) > 10^5. - _Robert Price_, Mar 04 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/2/21113.htm#prime">Prime numbers of the form 211...113</a>.

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

%F a(n) = A102948(n) - 1.

%e 2113 is prime, hence 2 is a term.

%o (PARI) a=23;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-17)

%o (PARI) for(n=0,1500,if(isprime((190*10^n+17)/9),print1(n,",")))

%Y Cf. A000533, A002275, A102948.

%K nonn,hard,more

%O 1,2

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 23 2004

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

%E a(20)-a(21) from _Robert Price_, Mar 04 2015

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Last modified April 25 05:18 EDT 2024. Contains 371964 sequences. (Running on oeis4.)