A101518 - OEIS

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

%S 0,1,2,7,8,18,57,120,186,805,854,1018,2592,2748,3015,4294,9663,14926,

%T 34561,64386,71298,71950

%N Indices of primes in sequence defined by A(0) = 67, A(n) = 10*A(n-1) - 63 for n > 0.

%C Numbers n such that 60*10^n + 7 is prime.

%C Numbers n such that digit 6 followed by n >= 0 occurrences of digit 0 followed by digit 7 is prime.

%C Numbers corresponding to terms <= 854 are certified primes.

%C a(23) > 2*10^5. - Robert Price, Sep 17 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/6/60007.htm#prime">Prime numbers of the form 600...007</a>.

%F a(n) = A103026(n-1) - 1.

%e 6007 is prime, hence 2 is a term.

%t For[n=1, n<=3000, n++, If[PrimeQ[60*10^n+7], Print[n]]] (Steinerberger)

%o (PARI) a=67;for(n=0,1200,if(isprime(a),print1(n,","));a=10*a-63)

%o (PARI) for(n=0,1200,if(isprime(60*10^n+7),print1(n,",")))

%Y Cf. A000533, A002275, A103026.

%K nonn,hard

%O 1,3

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

%E a(13)-a(15) from _Stefan Steinerberger_, Feb 03 2006

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

%E a(18)-a(22) from Kamada link by _Ray Chandler_, Apr 30 2015