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A056259 Indices of primes in sequence defined by A(0) = 77, A(n) = 10*A(n-1) - 13 for n > 0.

%I A056259 #32 Aug 15 2024 03:35:12
%S A056259 1,3,9,19,21,57,73,81,207,349,421,3811,3981,20923,23785,38851,56041,
%T A056259 68503,74433
%N A056259 Indices of primes in sequence defined by A(0) = 77, A(n) = 10*A(n-1) - 13 for n > 0.
%C A056259 Numbers n such that (680*10^n + 13)/9 is prime.
%C A056259 Numbers n such that digit 7 followed by n >= 0 occurrences of digit 5 followed by digit 7 is prime.
%C A056259 Numbers corresponding to terms <= 3981 are certified primes.
%D A056259 Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.
%H A056259 Patrick De Geest, <a href="http://www.worldofnumbers.com/deplat.htm#pdp757">PDP Reference Table - 757</a>.
%H A056259 Makoto Kamada, <a href="https://stdkmd.net/nrr/7/75557.htm#prime">Prime numbers of the form 755...557</a>.
%H A056259 <a href="/index/Pri#Pri_rep">Index entries for primes involving repunits</a>.
%F A056259 a(n) = A082713(n) - 2.
%e A056259 75557 is prime, hence 3 is a term.
%t A056259 Select[Range[0, 2000], PrimeQ[(680 10^# + 13) / 9] &] (* _Vincenzo Librandi_, Nov 03 2014 *)
%o A056259 (PARI) a=77;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a-13)
%o A056259 (PARI) for(n=0,1000,if(isprime((680*10^n+13)/9),print1(n,",")))
%Y A056259 Cf. A000533, A002275, A082713.
%K A056259 nonn,hard,more
%O A056259 1,2
%A A056259 _Robert G. Wilson v_, Aug 18 2000
%E A056259 Additional comments from _Klaus Brockhaus_ and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 03 2004
%E A056259 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, Jun 05 2007
%E A056259 More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
%E A056259 Three more terms added from Table, a link added, and comments section updated by _Patrick De Geest_, Nov 02 2014
%E A056259 Edited by _Ray Chandler_, Nov 05 2014