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A102007 Indices of primes in sequence defined by A(0) = 17, A(n) = 10*A(n-1) - 63 for n > 0. 1

%I #17 Nov 28 2021 03:03:18

%S 0,1,3,7,8,23,59,109,133,221,411,699,998,1382,5075,5542,6343,14599,

%T 15092,21716,23635,30220,50710,221627,350070,371695,487290,995255

%N Indices of primes in sequence defined by A(0) = 17, A(n) = 10*A(n-1) - 63 for n > 0.

%C Numbers n such that 10*10^n + 7 is prime.

%C Numbers n such that digit 1 followed by n >= 0 occurrences of digit 0 followed by digit 7 is prime.

%C Numbers corresponding to terms <= 998 are certified primes.

%C a(24) > 2*10^5. - _Robert Price_, Nov 09 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/1/10007.htm#prime">Prime numbers of the form 100...007</a>.

%F a(n) = A088274(n) - 1.

%e 10007 is prime, hence 3 is a term.

%t Select[Range[0, 100000], PrimeQ[10*10^# + 7] &] (* _Robert Price_, Nov 09 2015 *)

%o (PARI) a=17;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a-63)

%o (PARI) for(n=0,1500,if(isprime(10*10^n+7),print1(n,",")))

%Y Cf. A000533, A002275, A088274.

%K nonn,hard,more

%O 1,3

%A _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004

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

%E a(24)-a(28) added from A088274 by _Amiram Eldar_, Nov 28 2021

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Last modified March 29 09:32 EDT 2024. Contains 371268 sequences. (Running on oeis4.)