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A056257 Indices of primes in sequence defined by A(0) = 77, A(n) = 10*A(n-1) - 43 for n > 0.

%I A056257 #32 Jan 14 2023 13:49:27
%S A056257 1,3,7,27,63,723,1785,7275,19461,24213,51777,131391
%N A056257 Indices of primes in sequence defined by A(0) = 77, A(n) = 10*A(n-1) - 43 for n > 0.
%C A056257 Numbers n such that (650*10^n + 43)/9 is prime.
%C A056257 Numbers n such that digit 7 followed by n >= 0 occurrences of digit 2 followed by digit 7 is prime.
%C A056257 Numbers corresponding to terms <= 1785 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.
%C A056257 a(13) > 200000. - _Tyler Busby_, Jan 14 2023
%D A056257 Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.
%H A056257 Patrick De Geest, <a href="http://www.worldofnumbers.com/deplat.htm#pdp727">PDP Reference Table - 727</a>.
%H A056257 Makoto Kamada, <a href="https://stdkmd.net/nrr/7/72227.htm#prime">Prime numbers of the form 722...227</a>.
%H A056257 <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F A056257 a(n) = A082711(n) - 2.
%e A056257 72227 is prime, hence 3 is a term.
%o A056257 (PARI) a=77;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a-43)
%o A056257 (PARI) for(n=0,1000,if(isprime((650*10^n+43)/9),print1(n,",")))
%Y A056257 Cf. A000533, A002275, A082711.
%K A056257 nonn,hard,more
%O A056257 1,2
%A A056257 _Robert G. Wilson v_, Aug 18 2000
%E A056257 Additional comments from _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 03 2004
%E A056257 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, Jun 08 2007
%E A056257 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
%E A056257 One more term added from PDP table and comments section updated by _Patrick De Geest_, Nov 02 2014
%E A056257 Edited by _Ray Chandler_, Nov 05 2014
%E A056257 a(12) from _Tyler Busby_, Jan 11 2023