%I #29 Mar 06 2020 10:46:45

%S 11,13,17,19,101,103,107,109,1001,1003,1007,1009,10001,10003,10007,

%T 10009,100001,100003,100007,100009,1000001,1000003,1000007,1000009,

%U 10000001,10000003,10000007,10000009,100000001,100000003,100000007,100000009,1000000001,1000000003,1000000007,1000000009

%N Numbers of the form 10^n + 1, 3, 7, or 9 for n>=1.

%C A 10-automatic sequence: terms match the regular expression 10*[1379]. - _Charles R Greathouse IV_, Oct 15 2012

%C Primes in the sequence are at positions 1 to 8, 12, 15, 16, 18, 22, 31, 35, 36, 42, 66, 70, 72, 88, 95,... _R. J. Mathar_, Oct 16 2012

%H <a href="/index/Ar#10-automatic">Index entries for 10-automatic sequences</a>.

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,11,0,0,0,-10).

%F a(4n+r) = 10^(n+1) + k, (r, k) = (1, 1), (2, 3), (3, 7) or (4, 9).

%F G.f. -x*(-11-13*x-17*x^2-19*x^3+20*x^4+40*x^5+80*x^6+100*x^7) / ( (x-1)*(1+x)*(1+x^2)*(10*x^4-1) ). a(n)= 11*a(n-4) -10*a(n-8). - _R. J. Mathar_, Oct 16 2012

%p A088265 := proc(n)

%p if n <=8 then

%p op(n,[11,13,17,19,101,103,107,109]) ;

%p else

%p 11*procname(n-4)-10*procname(n-8) ;

%p end if;

%p end proc: # _R. J. Mathar_, Oct 16 2012

%t Flatten @ Table[10^n + m, {n, 50}, {m, {1, 3, 7, 9}}]. (* _Mikk Heidemaa_, Mar 06 2020 *)

%o (PARI) A088265(n)=10^((n+3)\4)+[9,1,3,7][n%4+1] \\ _M. F. Hasler_, Oct 15 2012

%Y Cf. A088266, A000533.

%K base,nonn,easy

%O 1,1

%A _Amarnath Murthy_, Sep 28 2003

%E More terms from _Max Alekseyev_, Oct 14 2012