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A270346 a(n) is the number whose base-11 digits are, in order, the first n terms of the simple periodic sequence: repeat 2,3,5,7.

%I A270346 #25 Sep 08 2022 08:46:16
%S A270346 2,25,280,3087,33959,373552,4109077,45199854,497198396,5469182359,
%T A270346 60161005954,661771065501,7279481720513,80074298925646,
%U A270346 880817288182111,9688990170003228,106578891870035510,1172367810570390613,12896045916274296748,141856505079017264235
%N A270346 a(n) is the number whose base-11 digits are, in order, the first n terms of the simple periodic sequence: repeat 2,3,5,7.
%C A270346 The periodic sequence comprises the first four primes, and the selected base is the fifth prime.
%H A270346 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (11,0,0,1,-11).
%F A270346 a(1)=2, a(2)=25, a(3)=280, a(4)=3087, a(5)=33959, a(n) = 11*a(n-1) + a(n-4) - 11*a(n-5). - _Harvey P. Dale_, Mar 15 2016
%F A270346 G.f.: x*(2+3*x+5*x^2+7*x^3) / ((1-x)*(1+x)*(1-11*x)*(1+x^2)). - _Colin Barker_, Jul 31 2016
%e A270346 a(8) = 45199854 = 23572357_11.
%t A270346 Table[FromDigits[PadRight[{},n,{2,3,5,7}],11],{n,30}] (* or *) LinearRecurrence[{11,0,0,1,-11},{2,25,280,3087,33959},31]
%o A270346 (PARI) a(n) = (-2074+305*(-1)^n+(370+410*I)*(-I)^n+(370-410*I)*I^n+1029*11^n)/4880 \\ _Colin Barker_, Jul 31 2016
%o A270346 (PARI) Vec(x*(2+3*x+5*x^2+7*x^3)/((1-x)*(1+x)*(1-11*x)*(1+x^2)) + O(x^30)) \\ _Colin Barker_, Jul 31 2016
%o A270346 (Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( x*(2+3*x+5*x^2+7*x^3)/((1-x^4)*(1-11*x)) )); // _G. C. Greubel_, Jul 14 2019
%o A270346 (Sage) a=(x*(2+3*x+5*x^2+7*x^3)/((1-x^4)*(1-11*x))).series(x, 30).coefficients(x, sparse=False); a[1:] # _G. C. Greubel_, Jul 14 2019
%o A270346 (GAP) a:=[2,25,280,3087,33959];; for n in [6..30] do a[n]:=11*a[n-1]+a[n-4]-11*a[n-5]; od; a; # _G. C. Greubel_, Jul 14 2019
%Y A270346 Cf. A033113.
%K A270346 nonn,easy,base
%O A270346 1,1
%A A270346 _Harvey P. Dale_, Mar 15 2016