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A101568 Indices of primes in sequence defined by A(0) = 53, A(n) = 10*A(n-1) - 27 for n > 0. 1

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

%S 0,1,2,7,17,19,30,41,102,174,180,530,705,1076,1176,1551,19736,32196,

%T 51507,58274,62232,90032

%N Indices of primes in sequence defined by A(0) = 53, A(n) = 10*A(n-1) - 27 for n > 0.

%C Numbers n such that 50*10^n + 3 is prime.

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

%C Numbers corresponding to terms <= 705 are certified primes.

%C a(23) > 2*10^5. - _Robert Price_, Aug 03 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/5/50003.htm#prime">Prime numbers of the form 500...003</a>.

%F a(n) = A096254(n) - 1.

%e 5003 is prime, hence 2 is a term.

%t Select[Range[0, 200000], PrimeQ[50*10^# + 3] &] (* _Robert Price_, Aug 03 2015 *)

%o (PARI) a=53;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-27)

%o (PARI) for(n=0,1500,if(isprime(50*10^n+3),print1(n,",")))

%Y Cf. A000533, A002275, A096254.

%K nonn,more

%O 1,3

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 09 2004

%E 1551 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 01 2008

%E a(17)-a(22) from Kamada data by _Ray Chandler_, Apr 30 2015

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Last modified March 28 10:55 EDT 2024. Contains 371241 sequences. (Running on oeis4.)