This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A079505 #29 Feb 12 2023 16:32:30
%S A079505 14,25,61,121,211,337,505,721,991,1321,1717,2185,2731,3361,4081,4897,
%T A079505 5815,6841,7981,9241,10627,12145,13801,15601,17551,19657,21925,24361,
%U A079505 26971,29761,32737,35905,39271,42841,46621,50617,54835,59281,63961,68881
%N A079505 The last number for which a determinant of base-n numbers is nonzero.
%C A079505 Suppose the number k written in base b requires N digits. We build A_k, a square N X N matrix with the digits of k, k-1,...,k-N+1 in base b. The number Det[A_k] is 0 for k greater than b^3-b+1 (except if b=2).
%C A079505 |Det[A_k]| is at most (b-1)^2. The last nonzero value is 1-b, which occurs for k = b^3-b+1 (cf. A061600) except for b=2, though I did not prove it.
%H A079505 Muniru A Asiru, <a href="/A079505/b079505.txt">Table of n, a(n) for n = 2..5000</a>
%H A079505 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A079505 a(n) = n^3 - n + 1 (except for n=2, a(2)=14).
%F A079505 From _Chai Wah Wu_, Nov 30 2018: (Start)
%F A079505 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 6.
%F A079505 G.f.: x^2*(7*x^4 - 29*x^3 + 45*x^2 - 31*x + 14)/(x - 1)^4. (End)
%e A079505 a(3)=25 because the determinant sequence in base 3 is 1, 2, 2, -1, -1, 4, -2, -2, -2, 2, 0, 1, -1, 0, 1, -1, 0, -4, 4, 0, 2, -2, 0, 2, -2, 0, 0, 0, 0, 0, 0, 0, .... and Det[A_k]=0 for k > 25.
%p A079505 seq(coeff(series(x^2*(7*x^4-29*x^3+45*x^2-31*x+14)/(x-1)^4,x,n+1), x, n), n = 2 .. 35); # _Muniru A Asiru_, Nov 30 2018
%t A079505 Table[ls = {}; Do[nt = Length[IntegerDigits[k, b]]; Ak = Table[IntegerDigits[k - i, b, nt], {i, 0, nt - 1}]; AppendTo[ls, Det[Ak]], {k, 1, b^4}]; Position[ls, _?(#!=0&)][[ -1, 1]], {b, 2, 10}]
%t A079505 CoefficientList[Series[(7x^4 -29x^3 +45x^2 -31x +14)/(x-1)^4, {x, 0, 50}], x] (* _Vincenzo Librandi_, Dec 01 2018 *)
%t A079505 LinearRecurrence[{4,-6,4,-1},{14,25,61,121,211},40] (* _Harvey P. Dale_, Feb 12 2023 *)
%o A079505 (Magma) [14] cat [n^3-n+1: n in [3..50]]; // _Vincenzo Librandi_, Dec 01 2018
%o A079505 (PARI) vector(50, n, n++; if(n==2, 14, n^3-n+1)) \\ _G. C. Greubel_, Jan 18 2019
%o A079505 (Sage) [14] + [n^3-n+1 for n in (3..50)] # _G. C. Greubel_, Jan 18 2019
%o A079505 (GAP) Concatenation([14], List([3..50], n -> n^3-n+1)); # _G. C. Greubel_, Jan 18 2019
%Y A079505 Cf. A061600.
%K A079505 base,nonn,easy
%O A079505 2,1
%A A079505 _Carlos Alves_, Jan 21 2003
%E A079505 Edited by _T. D. Noe_, Jun 24 2009