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A125725 Numbers whose base-7 representation is 222....2.

%I A125725 #57 Jan 12 2025 17:35:58
%S A125725 0,2,16,114,800,5602,39216,274514,1921600,13451202,94158416,659108914,
%T A125725 4613762400,32296336802,226074357616,1582520503314,11077643523200,
%U A125725 77543504662402,542804532636816,3799631728457714,26597422099204000
%N A125725 Numbers whose base-7 representation is 222....2.
%H A125725 Davis Smith, <a href="/A125725/b125725.txt">Table of n, a(n) for n = 1..1000</a>
%H A125725 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-7).
%F A125725 a(n) = (7^(n-1) - 1)/3 = 2*A023000(n-1).
%F A125725 a(n) = 7*a(n-1) + 2, with a(1)=0. - _Vincenzo Librandi_, Sep 30 2010
%F A125725 G.f.: 2*x^2 / ( (1-x)*(1-7*x) ). - _R. J. Mathar_, Sep 30 2013
%F A125725 From _Davis Smith_, Apr 04 2019: (Start)
%F A125725 A007310(a(n) + 1) = 7^(n - 1).
%F A125725 A047522(a(n + 1)) = -1*A165759(n). (End)
%F A125725 E.g.f.: (exp(7*x) - 7*exp(x) + 6)/21. - _Stefano Spezia_, Jan 12 2025
%e A125725 base 7.......decimal
%e A125725 0..................0
%e A125725 2..................2
%e A125725 22................16
%e A125725 222..............114
%e A125725 2222.............800
%e A125725 22222...........5602
%e A125725 222222.........39216
%e A125725 2222222.......274514
%e A125725 22222222.....1921600
%e A125725 222222222...13451202
%e A125725 etc...........etc.
%p A125725 seq(2*(7^n-1)/6, n=0..25);
%t A125725 FromDigits[#,7]&/@Table[PadLeft[{2},n,2],{n,0,25}]  (* _Harvey P. Dale_, Apr 13 2011 *)
%t A125725 (7^(Range[25]-1) - 1)/3 (* _G. C. Greubel_, May 23 2019 *)
%o A125725 (PARI) vector(25, n, (7^(n-1)-1)/3) \\ _Davis Smith_, Apr 04 2019
%o A125725 (Magma) [0] cat [n:n in [1..15000000]| Set(Intseq(n,7)) subset [2]]; // _Marius A. Burtea_, May 06 2019
%o A125725 (Magma) [(7^(n-1)-1)/3: n in [1..25]]; // _Marius A. Burtea_, May 06 2019
%o A125725 (Sage) [(7^(n-1) -1)/3 for n in (1..25)] # _G. C. Greubel_, May 23 2019
%o A125725 (GAP) List([1..25], n-> (7^(n-1) -1)/3); # _G. C. Greubel_, May 23 2019
%Y A125725 Cf. A007310, A023000, A047522, A165759.
%Y A125725 Cf. also A002276, A005610, A020988, A024023, A125831, A125835, A125857 for related or similarly constructed sequences.
%K A125725 easy,nonn,base
%O A125725 1,2
%A A125725 _Zerinvary Lajos_, Feb 02 2007
%E A125725 Offset corrected by _N. J. A. Sloane_, Oct 02 2010