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 A068601 #90 Jun 03 2025 01:09:08
%S A068601 0,7,26,63,124,215,342,511,728,999,1330,1727,2196,2743,3374,4095,4912,
%T A068601 5831,6858,7999,9260,10647,12166,13823,15624,17575,19682,21951,24388,
%U A068601 26999,29790,32767,35936,39303,42874,46655,50652,54871,59318,63999,68920
%N A068601 a(n) = n^3 - 1.
%C A068601 a(n) is the least positive integer k such that k can only contain 'n-1' in exactly 2 different bases B, where 1 < B <= k.
%C A068601 Apart from the first term, the same as A135300. - _R. J. Mathar_, Apr 29 2008
%C A068601 A058895(n)^3 + a(n)^3 + A033562(n)^3 = A185065(n)^3. - _Vincenzo Librandi_, Mar 13 2012
%C A068601 Numbers k such that for every nonnegative integer m, k^(3*m+1) + k^(3*m) is a cube. - _Arkadiusz Wesolowski_, Aug 10 2013
%H A068601 Nathaniel Johnston, <a href="/A068601/b068601.txt">Table of n, a(n) for n = 1..10000</a>
%H A068601 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A068601 Partial sums of A003215, hex (or centered hexagonal) numbers: 3*n(n+1)+1. - _Jonathan Vos Post_, Mar 16 2006
%F A068601 G.f.: x^2*(7-2*x+x^2)/(1-x)^4. - _Colin Barker_, Feb 12 2012
%F A068601 4*a(m^2-2*m+2) = (m^2-m+1)^3 + (m^2-m-1)^3 + (m^2-3*m+3)^3 + (m^2-3*m+1)^3. - _Bruno Berselli_, Jun 23 2014
%F A068601 a(n) = Sum_{i=1..n-1} (i+1)^3 - i^3. - _Wesley Ivan Hurt_, Jul 23 2014
%F A068601 Sum_{n>=2} 1/a(n) = Sum_{n>=1} (zeta(3*n) - 1) = A339604. - _Amiram Eldar_, Nov 06 2020
%F A068601 Product_{n>=2} (1 + 1/a(n)) = 3*Pi*sech(sqrt(3)*Pi/2). - _Amiram Eldar_, Jan 20 2021
%F A068601 E.g.f.: 1 + exp(x)*(x^3 + 3*x^2 + x - 1). - _Stefano Spezia_, Jul 06 2021
%e A068601 For n=6; 215 written in bases 6 and 42 is 555, 55 and (555, 55) are exactly 2 different bases.
%p A068601 A068601:=n->n^3-1: seq(A068601(n), n=1..50); # _Wesley Ivan Hurt_, Jul 23 2014
%t A068601 f[n_]:=n^3-1;f[Range[60]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 14 2011*)
%t A068601 LinearRecurrence[{4,-6,4,-1},{0,7,26,63},50] (* _Vincenzo Librandi_, Mar 11 2012 *)
%t A068601 Range[50]^3 - 1 (* _Wesley Ivan Hurt_, Jul 23 2014 *)
%o A068601 (PARI) a(n)=n^3-1
%o A068601 (Magma) [n^3-1: n in [1..40]]; // _Vincenzo Librandi_, Mar 11 2012
%o A068601 (GAP) List([1..45],n->n^3-1); # _Muniru A Asiru_, Oct 23 2018
%o A068601 (Python) for n in range(1,50): print(n**3-1, end=', ') # _Stefano Spezia_, Nov 21 2018
%Y A068601 Cf. A000217, A003215, A005448, A016921, A033562, A058895, A129294, A135300, A185065, A339604.
%K A068601 nonn,easy
%O A068601 1,2
%A A068601 _Naohiro Nomoto_, Mar 28 2002