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A056260 Indices of primes in sequence defined by A(0) = 77, A(n) = 10*A(n-1) - 3 for n > 0. Numbers n such that (690*10^n + 3)/9 is prime.

%I A056260 #31 Sep 08 2022 08:45:01
%S A056260 3,5,53,95,453,573,3383,11439,12623,19445,35459,81213,95325
%N A056260 Indices of primes in sequence defined by A(0) = 77, A(n) = 10*A(n-1) - 3 for n > 0. Numbers n such that (690*10^n + 3)/9 is prime.
%C A056260 Numbers n such that digit 7 followed by n >= 0 occurrences of digit 6 followed by digit 7 is prime.
%C A056260 Numbers corresponding to terms <= 3383 are certified primes.
%D A056260 Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.
%H A056260 Patrick De Geest, <a href="http://www.worldofnumbers.com/deplat.htm#pdp767">PDP Reference Table - 767</a>.
%H A056260 Makoto Kamada, <a href="https://stdkmd.net/nrr/7/76667.htm#prime">Prime numbers of the form 766...667</a>.
%F A056260 a(n) = A082714(n) - 2.
%e A056260 76667 is prime, hence 3 is a term.
%t A056260 Select[Range[3500], PrimeQ[(690 10^# + 3) / 9] &] (* _Vincenzo Librandi_, Nov 03 2014 *)
%o A056260 (PARI) a=77;for(n=0,1000,if(isprime(a),print1(n,","));a=10*a-3)
%o A056260 (PARI) for(n=0,1000,if(isprime((690*10^n+3)/9),print1(n,",")))
%o A056260 (Magma) [n: n in [0..300] | IsPrime((690*10^n+3) div 9)]; // _Vincenzo Librandi_, Nov 03 2014
%Y A056260 Cf. A000533, A002275, A082714.
%K A056260 hard,nonn
%O A056260 1,1
%A A056260 _Robert G. Wilson v_, Aug 18 2000
%E A056260 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, Apr 29 2007, Jun 15 2007
%E A056260 a(7)-a(11) from _Robert G. Wilson v_, May 02 2007
%E A056260 Two more terms added from PDP Table, a link added and comments section updated by _Patrick De Geest_, Nov 02 2014
%E A056260 Edited by _Ray Chandler_, Nov 05 2014